In a food processor, pulse flour, 1/4 cup granulated sugar, 1/4 cup brown sugar, and salt until combined.
Add cold butter cubes and pulse until mixture resembles coarse crumbs.
Add egg and vanilla, pulse until dough comes together.
Wrap dough in plastic and chill for 1 hour.
Meanwhile, mix diced apples with 1/4 cup brown sugar, cinnamon, nutmeg, and allspice for the filling.
Preheat oven to 350°F (175°C).
Roll out dough to 1/8 inch thickness and cut into 3-inch circles.
Place a spoonful of apple filling in the center of each circle.
Fold edges up to create a little tart, pinching to seal.
Bake for 15-18 minutes until golden brown.