• Preheat oven to 350F (175C) and line a 9x9-inch metal baking pan with parchment paper (or lightly grease with butter). Set aside.

Make the crust

• In a medium-sized mixing bowl, combine butter and sugar and use an electric mixer to beat until creamy and well combined.
  ½ cup (113 g) unsalted butter, ⅓ cup (67 g) granulated sugar
• Add flour and salt and, with mixer on low-speed, stir until mixture is crumbly and clings together if pinched between your thumb and forefinger.
  1 ½ cups (190 g) all-purpose flour, ½ teaspoon table salt
• Scatter crumbly dough evenly into prepared pan and use your hands or the back of a spoon to press into an even layer.
• Pierce all over with the tines of a fork then transfer to center rack of preheated oven and bake for 20 minutes, or until lightly golden. While the crust bakes, prepare your filling.
• Once crust has finished baking, remove from oven (but don’t turn off the oven) and set aside.

Prepare the filling

• In a medium saucepan, stir together apples, sugars, butter, lemon juice, flour, cinnamon, and salt.
  4 cups (425 g) peeled, cored, and thinly-sliced Granny Smith apples (sliced ⅛”-¼” thick), ¼ cup (50 g) light brown sugar, ¼ cup (50 g) granulated sugar, 2 Tablespoons unsalted butter, 1 Tablespoon lemon juice, 1 ½ Tablespoons all-purpose flour, 1 ½ teaspoons ground cinnamon, ¼ teaspoon table salt
• Cook over medium-low heat, stirring frequently, until butter is melted, then increase heat to medium and bring to a simmer. Cook until apples have softened slightly and the sauce has thickened enough to coat them. (There shouldn’t be a great deal of excess liquid remaining in the pan or the bars could become soggy).
• Remove from heat and stir in vanilla extract. Set aside while you prepare the topping.
  ½ teaspoon vanilla extract

Prepare the topping

• In a medium mixing bowl, whisk together flour, brown sugar, and salt.
  1 cup (125 g) all-purpose flour, ½ cup (100 g) light brown sugar, ¼ teaspoon table salt
• Scatter the cold butter pieces over the dry ingredients and use a pastry cutter to work together until butter is cut into pea-sized pieces. Add walnuts and continue to cut until you have a topping that is crumbly but clings to itself when pressed between thumb and forefinger.
  6 Tablespoons unsalted butter, ⅔ cup (70 g) chopped walnuts

Assemble

• Pour the apple mixture evenly over the baked crust.
• Scatter the topping evenly over the apples.
• Transfer to center rack of preheated oven and bake for 25-30 minutes, until topping is beginning to turn golden brown and apples are tender if pierced into with a toothpick.
• Allow bars to cool completely in the pan before slicing and serving (bars will be quite soft and fragile if sliced when warm). For neater slices, refrigerate before slicing and serving (not required).