Make the filling: Melt the butter in a medium saucepan over medium heat. Stir in the apples, brown sugar, flour, bourbon, water and cinnamon. Cover and cook, stirring often, until the apples are soft and the sauce is thick, about 10 minutes. (Add a splash more water if the apples are sticking.) Remove from the heat; set aside.
Make the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with liners. Whisk the flour, cinnamon, baking powder, baking soda and salt in a medium bowl. Whisk the melted butter, granulated sugar, brown sugar, sour cream, eggs and vanilla in a large bowl. Add the flour mixture and whisk until just combined.
Divide the batter among the prepared muffin cups, filling each about two-thirds of the way. Bake 12 minutes and remove from the oven. Drop 1 tablespoon of the apple filling on top of each cupcake, then continue baking until the cupcakes are golden around the edges, about 8 more minutes (it¿s OK if they still look a bit wet). Let cool 5 minutes in the pan, then transfer the cupcakes to a rack to cool completely.
Make the lattice crusts: Line a baking sheet with parchment paper. Unroll the pie dough on a cutting board. Cut into 1/4- to 1/2-inch strips and arrange in a lattice pattern. Cut out twelve 2-inch rounds from the lattice using a cookie cutter; place on the prepared baking sheet. Brush with the beaten egg and sprinkle with the coarse sugar. Bake until golden, about 15 minutes. Let cool completely on the baking sheet.
Make the frosting: Beat the heavy cream, sour cream and confectioners' sugar in a large bowl with a mixer on medium-high speed until stiff peaks form, 4 minutes. Spread on the cupcakes; top each with a lattice crust.