Roll the dough out on a floured surface until it is 1/8-inch thick. Using an 11 cm (8 ½ cm) round cookie cutter, cut 10 circles out of the dough and press them into the bottom and sides of a muffin tin. Using an 8 ½ cm round cookie cutter, cut out 10 more circles and set them on a sheet of parchment paper. Place both the muffin tin and the 10 additional circles in the fridge.
In a large bowl, combine the apples, 1/3 cup sugar, lemon zest and juice, flour, cinnamon, nutmeg and cloves. Divide the apple mixture between the pies and divide the diced butter between all pies.
Top each pie with another dough circle, and press the edges to seal both layers of dough together, then crimp with a fork. Slice an X-shape in the top of each pie to release steam while baking and brush with the beaten egg. Sprinkle some sugar on top of each pie.
Bake the pies at 400F for 30-40 minutes until the crust is golden brown and the filling is bubbling.
Allow the pies to cool for 10 minutes in the pan, then transfer to a wire rack. These taste best when eaten warm.