Place the flour, rosemary (if using), sugar, and salt in a food processor; pulse to mix. Add the cold butter cubes and pulse until the mixture has a sandy texture.

While the processor runs, add the ice water one tablespoon at a time until the dough forms a cohesive mass.

Transfer the dough to a sheet of plastic wrap, wrap it tightly, and chill in the refrigerator for 30 minutes.

Dust your work surface with flour. Roll the dough to a thickness of 1/4 inch. Using a 4-inch round cutter or a glass, stamp out circles. Gather the scraps, reroll, and cut more circles until you have 12 in total. Press each circle into a cup of a muffin tin, covering the bottom and sides. Reserve any leftover dough for the lattice or decorative tops.

Heat the oven to 425°F (220°C).

In a large bowl, combine the diced apples, granulated sugar, brown sugar, cinnamon, and flour; toss until the apples are evenly coated.

Spoon the apple mixture equally into the muffin cups. Place a lattice or cut-out shapes made from the reserved dough over the filling.

Brush the tops with the egg wash and, if desired, sprinkle with coarse sugar.

Bake for 16 to 18 minutes, until the pies are golden brown.

Take the tin out of the oven and allow the pies to cool completely in the pan.

Slide a sharp knife around the edge of each pie to loosen it, then lift out and serve.