Preheat the oven to 375 degrees. Prepare a non-stick 8×8 square baking pan by lining it with parchment paper cut 8 inches wide but long enough to hang over two edges of the pan. This will make removing the bars from the pan very easy!

For the crust, using a stand mixer fitted with the paddle attachment or a hand mixer, place butter, sugars and vanilla in the bowl and beat on medium speed for 2 minutes, or until lightened in color and creamy. Whisk together flour, salt, cinnamon and walnuts and slowly add to the butter-sugar mixture, with the mixer on low speed. Beat until just combined. Scatter two-thirds of the dough into prepared baking pan and press down lightly so that it covers the bottom and 1/2 inch up the sides. Reserve the remaining 1/3 dough for topping. Refrigerate pan for 20 minutes and then remove from fridge and bake for 18 to 20 minutes, until the crust is golden brown. Set aside to cool.

While crust is refrigerating and cooking prepare the filling. Melt the butter in a large, heavy pot and then add the apples, lemon juice, sugar, cinnamon and nutmeg. Cook on medium-low heat, stirring often, for about 15 minutes. The apples will be tender and most of the liquid will have evaporated. Add the cornstarch in the last minute of cooking and stir until thickened. Remove apples from heat and spread evenly over the baked crust, leaving a 1/2-inch border.

Smush pieces of the remaining dough with your fingers and scatter evenly on top of the apples (they will not be covered completely). Bake for 25 to 30 minutes, until the topping is browned. Cool, lift out of pan using parchment handles and cut into bars.