In a large saucepot (with lid) or Dutch oven, combine the apples, brown sugar, cinnamon, nutmeg, salt, and cornstarch. Stir until well combined.

Cover and cook over medium heat until apples begin to turn soft, about 13-15 minutes.

Remove from heat, add lemon juice and vanilla extract, and stir. Set aside and let cool.

In another saucepan, add cranberries, granulated sugar, and water. Stir until well combined.

Cook over medium-high heat for 10-12 minutes, or until cranberries start to break down. Set aside and let cool.

Roll out first portion of pie dough into a circle approximately 11" in diameter. Transfer dough into pie pan.

Stir together the apple and cranberry mixtures and then fill pie pan with filling.

Roll out the remaining portion of pie dough into a circle approximately 10" in diameter. Transfer to the top of the pie.

Brush edges with beaten egg and press together. Crimp edges as desired.

{Optional} If additional scraps of pie dough remain, roll them out and use a cookie cutter to cut into shapes. Brush one side with egg and press gently onto top of pie.

Brush top of entire pie (including edges) with beaten egg. Sprinkle with coarse sugar.

Bake at 400°F for about 60 minutes, or until crust turns golden brown. (Note: If necessary, cover edges with foil to prevent burning.)

Let pie cool for at least 1 hour before serving.