Preheat the oven to 350F and line a large baking sheet with parchment paper.
Using a very sharp large knife, cut the squash in half lengthwise and scoop out and discard seeds. Place cut side down on the prepared baking sheet. Bake 60 to 75 minutes, until tender. You should be able to squeeze the outside of the squash and feel it give.
Remove and use a large spoon to scoop the flesh into a medium bowl, reserving the skins. Add the butter and let melt in the hot squash, then add the Parmesan, garlic, basil, salt and pepper. Toss until well combined
Divide the mixture between the reserved skins and top with sliced Provolone or mozzarella. Return to the oven and bake another 8 to 10 minutes, or until cheese is melted and bubbly.