Cut the squash in half lengthwise. Scoop out the seeds. Rub olive oil on the flesh, then place the squash flesh-side down (skin-side up) on a foil-lined baking sheet. Roast in a 425°F oven for 35-40 minutes, or until tender when pierced with a fork.
While the squash roasts, melt 2 tablespoons of butter in a large skillet. Add the sliced apples and ¼ cup of the brown sugar. Sauté the apples until they're soft, about 10-15 minutes.
Use a slotted spoon to transfer the apples to a greased 2-quart or 3-quart casserole dish. Leave the juices from the apples in the skillet -- you don't need them in the casserole dish.
While the squash is still warm, but cool enough to handle, use a large spoon to scoop out the cooked flesh. Place the flesh in a food processor or blender. Add 2 tablespoons of butter, ¼ cup of brown sugar, and salt; process until smooth. You don't need to melt the butter, since the warm squash will melt it as they mix. Spread the whipped squash on top of the sautéed apples in the casserole dish.
Coarsely crush the Corn Flakes; place them in a small bowl. Add the chopped pecans and the remaining ¼ cup of brown sugar. Combine with 3 tablespoons of melted butter. Sprinkle the topping over the squash.
Bake, uncovered, at 350°F for 25 minutes, or until heated through. Keep a close eye on the casserole as it bakes, since the pecans have a tendency to burn easily. You may need to tent the top of the dish loosely with foil during the final 5-10 minutes to prevent excessive browning on top.