Mini Apple Pies

Name: Mini Apple Pies
Prep time: 20 min
Cook time: 30 min
Total time: 1 h
Yield: 12 mini pies
Ingredients: Ingredients; Crust; 2 1/2 cups all-purpose flour; 1 teaspoon salt; 1 tablespoon granulated sugar; 1 cup unsalted butter, cold and cubed; 6-8 tablespoons ice water; Apple Filling; 3 medium apples, peeled, cored, and diced (such as Granny Smith or Honeycrisp); 1/3 cup granulated sugar; 1/3 cup brown sugar; 1 teaspoon cinnamon; 1/4 teaspoon nutmeg; 1 tablespoon lemon juice; 1 tablespoon cornstarch; 1 tablespoon butter (optional, for richness); Assembly; 1 large egg, beaten (for egg wash); 1 tablespoon water; Optional: coarse sugar for sprinkling