In a bowl, mix the apples with the sugar, flour, cinnamon and vanilla. Cover and set aside while working on the puff pastry.
Unroll puff pastry onto a work surface. Cut into 36 small circles using a cookie cutter (1.75”). Gather the scraps and roll it again over a lightly floured surface to make more circles, if needed.
Press 18 of the circles into the cavities of a mini-muffin tin. They should come up the sides a bit.
Add apple mixture evenly to each of the muffin cups (about a teaspoon). Cover with the remaining 18 circles and press down around the edges (they will be lower than the top of the cavity). Brush the tops with the beaten egg.
Bake for 16 to 18 minutes, until golden brown and bubbly.
Let them cool in the pan for 20 minutes. Carefully loosen and remove from muffin tin.