Pull your pie crust out and allow to sit at room temperature to thaw for about 15 minutes
Melt butter in a medium sauce pan then slowly whisk in flour and simmer for a few minutes whisking constantly. Add in 1/4 cup of water, brown sugar, white sugar, lemon juice, and then bring to a slight boil but don't burn then reduce the heat and continue a light simmer for 4 minutes whisking frequently then remove from the heat.
Put apples in a large bowl then sprinkle cinnamon and vanilla on top and mix. Pour sauce over the apples and stir to coat the apples.
Put pie crust in a 9-inch baking dish then poke holes in the bottom with a fork and put in the oven for about 5 minutes then remove
Pour apple mixture into pie crust being careful not to get apples on edges of pie crust
Roll out top of pie crust with rolling pin on top of a flat surface. Then, place pie crust on top of pie filling (or you can look up a YouTube video of how to do a lattice top) then pinch edges closed. Cut 5 slits in top of pie crust.
Mix beaten egg with 1 tablespoon of granulated sugar then brush egg wash over crust and edges. Sprinkle with a few teaspoons of cinnamon and brown sugar.
Bake at 400 F for 15 minutes them reduce heat to 350 and bake another 35 minutes until apples are soft. Allow pie to cool for 1 hour before eating. Enjoy with French Vanilla Ice-cream.