Pick out a saucepan big enough for the two squash to fit in a single layer and fill with about an inch of water.
Bring to a boil, add the squash, cover, and cook for about 10 minutes.
Remove the squash with tongs and let cool for 5 minutes or so.
Cut off the tops of the squash and use a melon baller to scoop out the centers to create a good-sized cup for the filling. Discard the seedy filling, then chop up any squash flesh you scooped out and set it aside.
Preheat oven to 350°F.
Heat the olive oil in a skillet, then add the onion and peppers. Sauté until soft, about 5 minutes.
Add the chopped squash and cook for about a minute.
Remove from heat and add bread cubes, mozzarella, and Parmesan. Season with pepper and mix well.
Place the squash in the baking dish and stuff with the filling. You will have more stuffing than you need, but just let it overflow the squash.
Cover the baking pan loosely with foil and place in the oven to bake for about 15 minutes.