In a large sauté pan over medium-high heat, add EVOO, a turn of the pan, and the butter. When butter melts into oil, add onions, season with salt and pepper and stir. Cook to soften, about 5 minutes, then add apples and cook until tender, about 5 more minutes.
To assemble, cut hero rolls in half but not all the way through (like a book). Lay 1/4 pound of turkey in each roll, top with apple-onion mixture and 3 slices of cheese per hero. Place sammies on a baking sheet and broil until melted and bubbly, about 2 minutes.