Turn heat up to medium-high and add sweet potato. Cook until lightly browned on bottom and flip over.
When sweet potatoes are just getting tender, add zucchini, red pepper, and onion. Season with salt and pepper and add paprika, chili powder, and cayenne pepper. Cook until veggies are tender, stirring occasionally.
Remove from heat. Make 2 small wells and crack eggs into them. Place pan in oven and cook until eggs are cooked to your liking, about 5 to 10 minutes.