Place an apple half cut-side down on a cutting board and cut thin vertical slices into it, being careful not to slice all the way through. Repeat the process with the remaining apple halves. Transfer the apples to a 9-by-13-inch baking dish.
Melt 2 tablespoons of the butter in a small saucepot. Whisk in 2 tablespoons of the brown sugar until fully incorporated. Pour the butter and sugar mixture over the apples. Bake until the apples have softened, 18 to 20 minutes.
Meanwhile, make the streusel topping. In a small bowl, add the oats, flour, cinnamon, salt, remaining 2 tablespoons butter and remaining 3 tablespoons brown sugar. Using a fork or your hands, work the mixture together until it forms a large crumble.
Top each baked apple with the streusel topping, making sure to get some in between the apple slices. Return the dish to the oven and bake until the topping is golden brown, another 10 to 15 minutes. Serve the apples with a scoop of the ice cream.