Preheat oven to 350 degrees F (175 degrees C). Butter or spray a 3-quart casserole dish with cooking spray.
Stir butternut squash, 1/4 cup softened butter, 1 tablespoon brown sugar, salt, and pepper together in a bowl.
Melt 1 1/2 tablespoons butter in a large skillet over medium heat; stir in apples and white sugar. Cover skillet and simmer over low heat until apples are barely tender, 5 to 10 minutes.
Whisk flour, oats, 1/3 cup brown sugar, and cinnamon together in a bowl. Cut 1/4 cup butter into flour mixture using a pastry blender until mixture resembles coarse crumbs; stir in pecans.
Spread apple mixture into the prepared casserole dish. Spoon butternut squash mixture over apples; sprinkle with topping.
Bake in the preheated oven until bubbling and lightly browned, about 25 minutes.