Paper cupcake liners and a pastry bag or a large resealable plastic bag.
For the apple filling: Toss together the apples, granulated sugar, lemon juice, apple pie spice and salt in a medium bowl. Melt the butter in a medium skillet over medium heat. Add the apples and cook, stirring frequently, until the apples are tender but still pliable and the liquid is simmering, about 6 minutes. Add the flour and stir until it dissolves and the liquid thickens. Remove the skillet from the heat and let the filling cool completely. Divide the filling evenly into 12 little packed mounds within the skillet; set aside.
For the cupcakes: Position an oven rack in the center of the oven, and preheat the oven to 350 degrees F. Line a 12-cup muffin tin with paper liners and coat the liners and the top of the tin with cooking spray.
Whisk together the flour, baking powder, apple pie spice and salt in a medium bowl. In another medium bowl, beat the sugar and eggs with an electric mixer on medium-high speed until light and creamy, about 2 minutes. While continuing to beat, gradually pour in the butter, then add the vanilla. Adjust the mixer to medium-low and add half the flour mixture. Add the milk, then the remaining flour mixture, taking care not to overmix the batter. It will be thin, like pancake batter; transfer it to a liquid measuring cup to make filling the lined muffin cups easier.
Divide the batter evenly among the cups of the prepared muffin tin. Top each with a mound of apple filling. Bake for 15 minutes (the cupcakes will spread quite a bit). Remove the tin from the oven, gently brush the tops of the cupcakes with melted butter and sprinkle with granulated sugar. Continue to bake until the tops of the cupcakes, which will bake and puff around the apple filling, spring back when pressed, 6 to 8 minutes more. Let the cupcakes cool in the tin for a few minutes, then transfer to a rack to cool completely.
For the whipped topping: Beat the heavy cream, confectioners' sugar and sour cream in a medium bowl with an electric mixer on medium-high speed until the mixture forms soft peaks. Transfer it to a pastry bag or a resealable plastic bag with one corner snipped off. Pipe a dollop of whipped topping onto each cupcake (don't completely cover the cupcake) and sprinkle with apple pie spice.
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