Roast the squash: Preheat the oven to 425°F. Cut the butternut squash in half lengthwise and scoop out the seeds. Rub the flesh with olive oil, then place the squash cut-side down on a foil-lined baking sheet. Roast for 35-40 minutes, or until tender when pierced with a fork.
Cook the apples: While the squash roasts, melt 2 tablespoons of butter in a large skillet over medium heat. Add the sliced apples and ¼ cup of brown sugar. Cook, stirring occasionally, until the apples are soft, about 10-15 minutes.
Transfer the apples: Use a slotted spoon to transfer the apples to a greased 2- or 3-quart casserole dish, leaving the excess juices behind in the skillet.
Prepare the squash: When the roasted squash is cool enough to handle, scoop the cooked flesh into a food processor or blender. Add 2 tablespoons of butter, ¼ cup of brown sugar, and the salt. Process until smooth. Spread the whipped squash evenly over the apples in the casserole dish.
Make the topping: Coarsely crush the Corn Flakes and place them in a small bowl. Add the chopped pecans, remaining ¼ cup of brown sugar, and remaining 3 tablespoons of melted butter. Stir until combined.
Assemble: Sprinkle the Corn Flakes and pecan topping evenly over the squash.
Bake: Reduce the oven temperature to 350°F. Bake the casserole uncovered for about 25 minutes, or until heated through and golden brown on top. Watch the pecans closely and tent the dish loosely with foil during the final 5-10 minutes if the topping starts to brown too quickly.