Preheat broiler, setting it on “low.”
Meanwhile, in a small (8-inch) ovenproof skillet over medium heat, add 1 tablespoon oil and onions and bell peppers and cook until golden, about 5 minutes. Add the mushrooms and cook until soft, about 5 minutes. Transfer to a plate. Add 1 more tablespoon oil and sauté the spinach until wilted. Toss with the mushrooms mixture. Wipe the skillet clean and add the remaining oil, making sure to spread it evenly on the bottom and sides.
Pour 1/3 of the eggs and egg whites in and swirl to distribute evenly on bottom and sides. Scatter the sautéed vegetables all around and pour the remaining eggs and egg whites on top. Cook until the bottom is set and golden.
Then place the skillet in the oven to finish, allowing the eggs to rise and become golden, 3–4 minutes. Remove from oven, slide onto a cutting board or plate, and slice.