- Position a rack in the center of the oven and preheat to 450°F.
- Lightly oil a large baking sheet or roasting pan.
- Toss the potatoes, bell pepper, zucchini, onion and olive oil on the baking sheet and season to taste with salt and pepper.
- Bake, occasionally turning the vegetables with a spatula, until the potatoes are almost tender, about 40 minutes.
- Stir in the tomatoes, garlic and thyme.
- Bake until the vegetables are browned, about 20 minutes more.
- Transfer the vegetables to a 2-quart ovenproof serving dish.
- Spacing them evenly apart, break the eggs over the vegetables.
- Bake until the eggs are set, about 10 minutes.
- Sprinkle with the cheese and serve immediately.