In a food processor, pulse together 2 cups of flour and 1/4 teaspoon of salt.
Add the egg yolk, cubed butter, and milk. Pulse until a soft dough forms. If needed, add 1 more tablespoon of milk to bring the dough together.
Wrap the dough in plastic and refrigerate while preparing the filling.
Toss the diced apples with granulated sugar, light brown sugar, cinnamon, flour, and nutmeg.
Press the chilled dough into an 9-inch square baking pan lined with parchment. Add the apple mixture over the crust. Crumble the remaining dough over the apples.
Bake in a preheated oven at 350°F for about 45-55 minutes or until the crust is golden and the filling is bubbly.
Let the bars cool completely before cutting into squares. Serve as is or with a scoop of vanilla ice cream.