For the Crust:
For the Filling:
For the Topping:
Preheat the oven to 375° fahrenheit. Line a 12-by-17-inch rimmed baking sheet or jelly roll pan with parchment paper. In a standing electric mixer fitted with the paddle attachment, beat the butter with the sugar at medium speed until light and fluffy, about 2 minutes. At low speed, beat in the flour and salt until a soft dough forms. Press the dough over the bottom of the prepared pan and 1/2 inch up the side in an even layer. Bake in the center of the oven for about 20 minutes, until the crust is golden and set. Let cool on a rack.
In each of 2 large skillets (or one giant copper skillet that we randomly have), melt 3 tablespoons of the butter with 1/4 cup of the dark brown sugar. Add the apples to the skillets and cook over high heat, stirring occasionally, until softened, about 10 minutes. Stir half of the cinnamon, nutmeg and vanilla into each skillet. Cook until the apples are caramelized and very tender and the liquid is evaporated, about 10 minutes longer; scrape up any bits stuck to the bottom of the skillets and add up to 1/2 cup of water to each pan to prevent scorching. Let cool.
In a large bowl, mix the oats with the flour, dark brown sugar, cinnamon, baking soda and salt. Using a pastry blender or your hands, cut in the butter until the mixture resembles large peas. Stir in the walnuts and press the mixture into clumps.
Spread the apple filling over the crust. Scatter the crumbs on top, pressing them gently into an even layer. Bake in the center of the oven for 1 hour, until the topping is golden; rotate the pan halfway through baking. Let cool completely on a rack before cutting into 2-inch bars.