Preheat the oven to 375°F. Grease a 9×13 baking pan with butter or non-stick spray.
In a large bowl, combine 2½ cups of flour with 2 tablespoons of granulated sugar.
Using a pastry cutter, cut the cold butter into the flour mixture until it resembles coarse crumbs.
In a separate small bowl, whisk together the egg yolks and milk. Add this liquid mixture to the flour mixture and stir until a dough forms.
Reserve one-fourth of the dough for the topping.
Press the remaining dough evenly into the prepared baking pan to form the crust.
Arrange the sliced apples over the crust in an even layer.
In a small bowl, mix together ½ cup granulated sugar, ¼ cup brown sugar, and cinnamon. Sprinkle this mixture evenly over the apples.
For the crumb topping: Combine the reserved dough with 2 tablespoons of flour, 1 tablespoon of granulated sugar, 1 tablespoon of brown sugar, and the crushed pecans. Mix until crumbly.
Sprinkle the crumb topping evenly over the sugared apples.
Bake for approximately 40 minutes, or until the topping is golden brown and the edges are bubbly.
Allow the bars to cool in the pan before cutting into squares.
Serve warm or at room temperature. These bars are delicious on their own or with a scoop of vanilla ice cream!