The original recipe for this pastry is from The Good Huswifes Handmaid for Cookerie in her kitchen (1588):

For a tarte of apples and orange pilles. Take your orenges and lay them in water a day and a night, then seeth them in faire water and honey and let seeth till they be soft; then let them soak in the sirrop a day and a night: then take forth and cut them small and then make your tart and season your apples with suger, synamon and ginger and put in a piece of butter and lay a course of apples and between the same course of apples a course of orenges, and so, course by course, and season your orenges as you seasoned your apples with somewhat more sugar; then lay on the lid and put it in the oven and when it is almost baked, take Rosewater and sugar and boyle them together till it be somewhat thick, then take out the Tart and take a feather and spread the rosewater and sugar on the lid and let it not burn.
I had obtained a similar recipe electronically (From the usenet bboard rec.recipes), and used it as a starting point for my redaction:

9" pie shell and lid
4 medium apples, peeled, cored, and sliced
5 medium oranges
1/2 cup brown sugar
1 cup honey
1/4 tsp cinnamon
3 cup water
1/4 tsp salt
juice of 1/2 lemon
1/8 tsp ginger
1 tsp confectioners sugar, disolved in 1 Tbsp water
Bake shell at 425F for 10 minutes. Slice oranges thin, discarding seeds. Mix water, honey, and lemon juice, and bring to a boil. Add oranges, cover and simmer for 2 hours. Drain the oranges. Mix apples, sugar, spices, and salt. Put a layer of apples in the pan, then a layer of oranges, and so forth. Put on the lid, slash, and paint with rosewater/sugar mixture. Bake for 1 hour at 350F.
I used the original recipe as a procedural and ingredients guide, and the other recipe as quantity guide. Here's the results:

6 medium oranges. I used valencia oranges, though temple oranges, blood oranges, and seville oranges should all work as well. Both bitter (seville) and sweet oranges were available during the 16th C. Don't use navel oranges; the skins are too thick.
4 cups water
1 1/3 cup honey
14 small Macintosh apples. Any small cooking apple should do.
1 cup sugar
1 tsp cinnamon
1/2 tsp ginger
2 Tbsp rosewater
1 Tbsp sugar
1 9" pie crust and lid (If you use a storebought or a shortening and cold watercrust, bake it 10 minutes before adding stuff. If you use the crust recipe that appears with this redaction, there's no need to bake the crust beforehand)
Soak oranges in water for 24 hours. In a large saucepan, mix honey with 4 cups of the water used to soak the oranges, add the oranges, bring to a boil, and simmer until the peels on the oranges feel soft. Place the oranges in a container and pour on all the syrup. If there is not enough syrup to compleetly cover the oranges when weighted, add a little more water. Put a plate or other heavy object on top of the oranges to hold them under the syrup, cover your container, and let the oranges soak for 24 hours.

When you're ready to bake, preheat oven to 350F. Slice oranges and remove the seeds. If the syrup has not completely saturated the rinds, boil the slices in the syrup until the rinds are saturated (this should not be necessary). Chop the oranges into small pieces (I used a blender), and mix in 1/3 cup sugar, 1/2 tsp cinnamon, and 1/4 tsp ginger. Peel, core, and quarter your apples, mix them with the remaining sugar, cinnamon, and ginger. Make and roll your pie crust. Place a layer of apples on the bottom of the crust, cover with a layer of oranges. Repeat the layering until you're out of filling. (Typically, you'll get two layers of each) Put on the lid, crimp the edges, and bake for 1 hour.

Ten minutes before the pie finishes baking, mix your rosewater and sugar and stir over low heat until it becomes syruppy. Five minutes before the pie finishes baking, remove the pie from the oven, brush on the rosewater syrup, and return the pie to the oven until the hour is up.

As to the pie crust, the same Good Huswifes Handmaid includes recipe for that, too:

"To make paste and to raise coffins. Take fine flour and lay it on a board and take a certaine of yolkes of egges as your quantitie of flower is, then take a certain of Butter and water and boile them together but you muist take heed ye put not too many yolkes of egges, for if you doe it will make it dry and not pleasant in eating, and ye must take heed ye put not in too much Butter, for if you doe, it will make it so find and so short that you cannot raise: and this paste is good to raise all manner of coffins: likewise if ye bake veneson, bake it in the paste above named."
Gervase Markham, in The English Huswife, provides a similar crust recipe:

"... your fine wheat curst must be kneaded with as much butter as water, and the paste made reasonable lithe and gentle, into which you must put three or four eggs or more according to the quantity you blend together, for they will give it a sufficient stiffening."
These are both very similar to modern deep-dish pie and meat pie recipes. Here's the result:

For a 9" pie:

2 1/2 cup flour
1/2 cup butter
6 Tbsp water
3 egg yolks
Mix flour and egg yolks. Put butter and water in a small saucepan over low heat until the butter is melted. Add butter and water to flour and egg mixture. Knead until all flour is part of the dough ball. If extra water is needed, add 1 tsp water. Divide in half and roll. No chilling required!
The taste is similar to a shortening and cold-water crust, but the texture is stiffer and more solid.

So, eat and enjoy!

Gretchen Miller (Margaret MacDuibhShithe)/grm+@andrew.cmu.edu

Bibliography:

The Good Huswifes Handmaid for Cookerie in her kitchen (1588)

The English Houeswife: containing the inward and outward virtures which out to be in a complete woman; as her skill in physic, cookery, banqueting-stuff, distillation, perfumes, wool, hemp,flax dairies, brewing, baking, and all other things belonging to a household, // Gervase Markham (1615); edited by Michael R. Best, Kingston, Ontario: McGill-Queen's University Press, c1986

Food and Drink in Britian from the Stone Age to the 19th century; // C. Anne Wilson, Chicago: Academy Chicago Publishers, 1991