Heat the oil in a medium skillet over medium-high heat. Add the garlic and cook for 1 minute. Add the tomatoes, 1/2 teaspoon salt, and 1/4 teaspoon pepper and simmer for 5 minutes. Add the spinach and cook until it begins to wilt, 1 minute. Transfer to a 2-quart baking dish.
Beat the egg whites until foamy, about 30 seconds, then pour them over the spinach mixture. Carefully place the whole yolks over the top.
Bake until the whites are set, 20 to 22 minutes. Divide among individual plates.