Heat the oven to 375°F and grease six 5- to 6-ounce ramekins or six cups of a standard muffin pan. Place the vessels on a foil-lined baking sheet to catch any juices that bubble over.

Combine the apples, granulated sugar, flour, cinnamon, optional nutmeg, lemon juice, and salt in a bowl. Let the mixture stand for about 10 minutes so the apples release some juice and the flour begins coating the fruit.

Cut six pastry rounds about 5 to 6 inches wide, making each round large enough to line a ramekin or muffin cup with a little overhang. Press the pastry gently into the greased baking vessels without stretching it.

Divide the apple mixture among the pastry shells, taking care not to overfill them. Dot the top of each portion with the small pieces of unsalted butter.

Cut six smaller pastry rounds or strips for the tops and place them over the apples. Press or crimp the edges to seal, then cut a small vent in every top so steam can escape.

Beat the egg with the water to make an egg wash and brush it lightly over each pie. Sprinkle with coarse sugar if desired, then chill the assembled pies for 15–30 minutes, especially when using homemade pastry.

Bake for 25–35 minutes, until the pastry is golden brown and the apple filling is visibly bubbling. If the tops begin to brown too quickly, cover them loosely with foil for the remainder of the baking time.

Cool the pies for at least 10–15 minutes before serving. This short rest allows the filling to thicken and makes the pies easier to enjoy without losing their warm, soft texture.