1. Preheat the oven to 375 F. Line an 8-inch square baking pan with parchment paper, leaving an overhang on 2 opposite sides to make it really easy to remove when baked.

Make the pastry dough:

1. In a large mixing bowl, add flour, sugar, baking powder, salt, butter, and egg. Stir well with a fork or pastry cutter until the flour mixture forms into small crumbs. You can also combine all ingredients in a food processor and pulse mix until it resembles coarse crumbs.

Make the apple filling:

1. In a medium mixing bowl, mix together apples, sugar, and cornstarch until evenly coated.
2. Add apple mixture in a large saucepan and cook over medium heat until softened, stirring occasionally, about 5-7 minutes.
3. Add lemon juice, cinnamon, vanilla extract and butter. Stir well and bring it to a simmer. Simmer for 3-4 minutes until the apples are tender and the sauce is thickened. Set aside.

Assemble and Bake:

1. Spread half of the crumb mixture evenly into the prepared baking dish and press it to pack it and form an even bottom crust.
2. Spread the apple mixture evenly over the crust and add the remaining half of the crumb mixture on top.
3. Bake for 45-50 minutes until the crust turns golden brown. Serve it warm or let it cool at room temperature for about 30 minutes so that the filling can set. Letting it cool completely will make it easier to cut. You can speed up on the process by storing in the refrigerator or freezer for 1 hour to help it set faster.
4. Slice the apple crumb bars into 9 or 16 squares and serve warm with a scoop of vanilla ice cream on the side or serve cold.