Preheat and Prepare: Begin by setting your oven to 375 degrees Fahrenheit (190 degrees Celsius). Grease a 9 x 13-inch baking pan with butter or non-stick spray to prevent sticking.
Mix Dry Ingredients: In a large mixing bowl, combine 2 ½ cups of flour with 3 tablespoons of granulated sugar. Stir these dry ingredients together until they are well mixed.
Form the Dough: Utilize a pastry cutter to incorporate the cup of butter or shortening into the flour mixture until the mixture resembles coarse crumbs. In a separate bowl, whisk together the egg yolks and milk. Gradually add this liquid mixture to the flour mixture, stirring continuously until a dough forms.
Reserve Topping Dough: Set aside one-fourth of the dough to be used later for the crumb topping.
Assemble the Crust: Take the remaining dough and press it evenly into the bottom of the prepared baking pan, creating a firm base for the filling.
Prepare the Filling: Arrange the sliced apples over the crust. In a small bowl, mix together the brown sugar, granulated sugar, and cinnamon, then sprinkle this sugar mixture evenly over the apples.
Create the Crumb Topping: Combine the reserved dough with an additional tablespoon of brown sugar, crushed pecans, a tablespoon of granulated sugar, and two tablespoons of flour. Mix until crumbly and then sprinkle this mixture over the sugared apples.
Bake: Place the pan in the preheated oven and bake for approximately 40 minutes, or until the topping is golden brown and the filling is bubbly.
Cool and Serve: Allow the bars to cool in the pan before cutting into squares. This rest period helps the bars to set, making them easier to serve.