In a large bowl, combine the flour, salt, and sugar.

Add the cold, cubed butter to the flour mixture and work it into the flour until it resembles coarse crumbs.

Gradually add ice water, one tablespoon at a time, mixing until the dough comes together.

Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.

In a bowl, mix the diced apples with brown sugar, cinnamon, nutmeg, and lemon juice.

Preheat your oven to 375°F (190°C).

On a floured surface, roll out the chilled dough to about 1/8 inch thick.

Cut out circles from the dough and press them into the muffin tin cups.

Fill each with the apple mixture and top with another circle of dough. Seal the edges and brush with beaten egg.

Bake for 25 minutes or until golden brown.