Heat oil in a large skillet over medium-high heat. Add onion and potatoes and season with salt and pepper. Cook, stirring frequently, for about 15 minutes, or until potatoes are almost cooked through and golden brown.
Reduce heat to medium, add zucchini, garlic, thyme, and paprika. Cook about 7 minutes more, stirring, until zucchini is soft and potatoes are cooked through. Serve topped with four sunny side up eggs.