Peel, core, and slice 4 medium apples into even pieces. Toss them in a large bowl with 1 tablespoon of lemon juice to prevent browning and add brightness. Mix in 1/2 cup of brown sugar and 1/2 teaspoon of ground cinnamon until apples are well coated.
In a medium saucepan over medium heat, melt 1/2 cup of unsalted butter. Continue cooking, stirring frequently, until the butter foams, turns a golden brown, and releases a nutty aroma, about 4-5 minutes. Be careful not to burn it.
Remove the browned butter from heat and pour it into a mixing bowl. Add 1 cup rolled oats, 1/2 cup all-purpose flour, 1/4 cup granulated sugar, 1/4 teaspoon salt, and 1/2 cup chopped walnuts or pecans. Stir until the mixture is crumbly and evenly coated with the butter.
Preheat your oven to 350°F (175°C). Spread the apple mixture evenly in your baking dish. Sprinkle the crumble topping generously over the apples, covering them completely.
Bake the crumble for 40-45 minutes or until the topping is golden brown and crisp and the apples are bubbling around the edges. If the topping browns too quickly, cover loosely with foil halfway through baking.
Let the Brown Butter Apple Crumble cool for at least 10 minutes before serving. Serve warm on its own or with vanilla ice cream, whipped cream, or caramel sauce.