Begin by preheating your oven to 375°F (190°C).

To prepare the crust, combine the unsalted butter, granulated sugar, light brown sugar, and pure vanilla extract in the bowl of an electric mixer equipped with a paddle attachment. Beat these ingredients on medium speed for approximately 2 minutes, or until the mixture appears light and creamy. In a separate bowl, sift together the all-purpose flour and kosher salt. Gradually add this dry mixture to the butter-sugar combination while the mixer is set to low speed. Continue mixing until the ingredients are thoroughly blended.

Next, distribute two-thirds of the prepared dough in clumps across a 9 x 13-inch baking pan. Using floured hands, gently press the dough down into the bottom and up the sides of the pan, approximately 1/2 inch high. Refrigerate this crust for 20 minutes. Once chilled, bake it in the preheated oven for 18 to 20 minutes, or until the crust is golden brown. Set aside to cool once baked.

While the crust is cooling, return the remaining dough to the mixer. Add the chopped walnuts and ground cinnamon, mixing on low speed until evenly combined. Set this mixture aside for later use.

Lower the oven temperature to 350°F (175°C). In a large mixing bowl, combine the sliced Granny Smith and Golden Delicious apples with the freshly squeezed lemon juice. Sprinkle in the granulated sugar, ground cinnamon, and ground nutmeg, and stir well to incorporate all ingredients. In a large pot (approximately 10 inches in diameter), melt the unsalted butter over medium to medium-low heat. Add the apple mixture to the pot and simmer, stirring frequently, for 12 to 15 minutes or until the apples become tender and most of the liquid has evaporated.

Spread the cooked apple mixture evenly over the cooled crust, leaving a 1/2-inch border around the edges. Take pieces of the remaining dough and pinch them into medium-sized bits, then distribute these pieces evenly atop the apples—do not cover them entirely. Bake the assembled bars for 25 to 30 minutes, or until the topping turns a golden brown. Allow the bars to cool completely before slicing them into squares.