Melt butter in a saucepan over medium heat. Add apples; toss until coated with butter. Stir in brown sugar, white sugar, lemon juice, 1 1/2 teaspoons cinnamon, 1/2 teaspoon vanilla extract, salt, nutmeg, allspice, and cloves; cook and stir until apples have softened and sugars have melted, about 5 minutes. Bring to a boil.
Combine water and cornstarch in a bowl. Stir cornstarch mixture into the apple mixture; cook and stir until apple mixture is thickened, about 5 minutes. Remove from heat; cool completely, about 20 minutes.
Roll out 1 sheet of pie crust on a work surface with a rolling pin; cover with half of the cooled apple mixture. Roll out a second sheet of pie crust with a rolling pin; slice into 1/2-inch wide strips with a sharp knife. Weave pie crust strips together over apple mixture to create a lattice top.
Flour a round cookie cutter or drinking glass. Press cookie cutter through dough to create 12 round pies. Transfer to a baking sheet.
Bake in the preheated oven until crust is cooked through a golden brown, about 20 minutes. Transfer to a wire rack to cool, about 10 minutes.
Repeat with remaining pie crusts and apple mixture; place on a second baking sheet. Bake in the oven until crust is cooked through a golden brown, about 20 minutes.
Combine confectioners' sugar and 1 teaspoon cinnamon in a mixing bowl; add 1 teaspoon vanilla extract. Stir in milk slowly until desired consistency is reached; drizzle over cooled pies.