Preheat the oven to 350 degrees Fahrenheit and lightly butter a 9-inch square baking dish.

Peel the apples with a vegetable peeler, then cut them in half and remove the core with a sharp knife. Slice each half into half-inch thick pieces.

In a large mixing bowl, combine the sliced apples, granulated sugar, brown sugar, flour, cinnamon, nutmeg, and salt. Add the lemon juice and vanilla extract, then toss gently until the apples are evenly coated.

Pour the apple mixture into the prepared baking dish, spreading it in an even layer.

In a medium mixing bowl, whisk together the flour, brown sugar, salt, and cinnamon for the topping.

Add the cold butter cubes to the flour mixture and use your fingertips or a fork to work the butter into the dry ingredients until the mixture resembles coarse breadcrumbs.

Stir the chopped nuts into the topping mixture, then sprinkle it evenly over the apples.

Bake for 40 to 45 minutes, until the topping is deep golden brown and the apple filling is bubbling around the edges.

Let the crisp rest for 10 to 15 minutes before serving.