Brown the Butter: In a small saucepan over medium heat, melt the butter. Swirl constantly as it foams and crackles. After 4-5 minutes, golden-brown specks will settle at the bottom with a rich nutty aroma. Immediately transfer to a heat-safe bowl and let cool for 5 minutes.
Prep Oven & Skillet: Preheat your oven to 350°F (175°C). Lightly grease a 10-inch cast-iron skillet or an 8x8-inch ceramic baking dish with butter.
Toss the Apple Filling: In a large mixing bowl, toss the sliced apples with granulated sugar, dark brown sugar, ground cinnamon, nutmeg, fresh lemon juice, cornstarch, and pure vanilla extract until every slice is glossy and spiced.
Transfer Apples: Arrange the seasoned apples evenly into the prepared cast-iron skillet, pressing down gently into a compact layer.
Assemble Streusel Topping: In a medium bowl, stir together the rolled oats, all-purpose flour, packed brown sugar, chopped pecans, ground cinnamon, and flaky sea salt. Pour in the cooled brown butter. Toss with a fork until moist, clumpy streusel clusters form.
Scatter & Cover: Distribute the oat pecan streusel evenly over the apples, covering the surface from edge to edge.
Bake to Golden Perfection: Bake at 350°F for 35 to 40 minutes, until the apple juices are vigorously bubbling around the edges and the streusel topping is deep golden brown and fragrant.
Rest & Serve: Let the apple crisp cool for 10 minutes so the caramelized juices settle and thicken slightly. Serve warm in dessert bowls topped with a generous scoop of French vanilla bean ice cream.