Brown butter in a small pan over medium heat until milk solids are amber and smell nutty. Chill until firm but pliable.
Heat oven to 375°F; butter a 9-by-13-inch baking dish.
Toss apples with first brown sugar, 2 tablespoons flour, lemon juice, cinnamon, and 1/4 teaspoon salt. Spread in dish.
Mix remaining flour, remaining brown sugar, and 1/2 teaspoon salt; rub in cooled brown butter to form crumbs.
Scatter crumbs evenly over apples.
Bake 45 to 50 minutes until apples are tender, center bubbles, and crumbs brown. Rest 20 minutes.