Mix the flour, sugar, salt, pepper and cheddar cheese together the bowl of a food processor fitted with a blade. Pulse a few times to evenly disperse everything through the flour.
Slice the butter into thin slabs and add all at once to the food processor bowl. Pulse until the consistency is about the size of peas (about 10-12 pulses). A great way to check the consistency is by scooping up some of it with a fork.
Add the cider vinegar and 2 tablespoons of ice water and pulse 8 - 10 times, until the dough just starts to hold together when you pinch it between your fingers. If the dough doesn't hold together, add additional ice water in small amounts. Pour the contents of the food processor bowl out onto the counter or other work space and knead the dough until it starts to hold together and forms into a ball.
Divide the dough into double the number of pies / tarts you plan to make. So if you plan to make one big pie, divide the dough in two and form into discs. One disc should be larger than the other as you will need more dough for the pie bottom and sides than for the lattice.
Wrap the discs in wax paper and chill in the refrigerator for 30 minutes while you make the pie filling.
Preheat the oven to 400° F. Roll out the discs: there are a few ways to do this, but here's the easiest one I've ever found. Place a fresh sheet of wax paper on your work space. Place one of the discs on it and roll it out a few times. Cover it with another fresh sheet of wax paper and roll the dough to the desired thickness. After every few rolls, you may want to peel off one or both pieces of wax paper. Lay the wax paper back down on the dough and continue rolling. This method of rolling the dough between wax paper makes rolling quick work! And the less work you put on the dough, the more tender it will be in the end.
Once the dough is 1/8" thickness thick, peel off the wax paper from one side, flip the dough over the pie plate and gently peel off the wax paper on the other side. Tuck the dough down into the pie plate, taking care not to stretch it. Allow the dough to drape over the pie plate and cut off the excess with scissors or a knife. Shape the edges into flutes and pop the pie plate and dough into the freezer for 15 minutes. Freezing pie crust before baking helps to keep the fluted shape.
Now roll out the smaller disc of dough into a rectangle using the same wax paper process explained above. With a pizza slicer or a knife, slice into strips to be used for the lattice tops.
Fill the pie with the filling (recipe below) and lay down the strips, pressing the strip ends into the dough forming the bottoms and sides.
Lightly baste the dough with whole milk and sprinkle with turbinado sugar over the top of the entire pie.
Bake for 50 minutes, or until the apple slices soften and the filling is bubbling. You may want to check the browning of the pie crust after 25 minutes to determine if you need to cover it with foil for the balance of the baking. Allow to cool on a cooling rack.