Preheat the oven to 350°F.
Add flour, cold butter, salt, and 1 tablespoon of granulated sugar to a food processor. Pulse until the mixture resembles coarse crumbs.
Add the cold water and pulse until the dough begins forming a ball.
Refrigerate the dough for 10 to 15 minutes.
Roll the chilled dough into a rectangle on a lightly floured surface.
Brush the dough with milk and sprinkle with the remaining tablespoon of sugar.
Cut the dough into approximately 2-inch squares and arrange them on a baking sheet.
Bake for approximately 15 minutes, or until lightly golden. Set aside.
Meanwhile, melt 4 tablespoons of butter in a large skillet over medium heat.
Arrange the apple slices evenly in the skillet. Add the lemon juice, brown sugar, and salt.
Reduce the heat to low, cover, and cook for approximately 15 minutes, or until the apples are tender and juicy.
Sprinkle the cooked apples with cinnamon and nutmeg. Add additional lemon juice to taste, if desired.
Divide the warm apples among four individual serving dishes.
Drizzle each serving with caramel sauce, whipped cream or Vanilla Bean ice cream and arrange approximately four pastry squares around or over the apples.