My Eggs in Purgatory

Name: My Eggs in Purgatory
Ingredients: 2 tablespoons olive oil; 6 cloves garlic; 1 large white onion; 1 carrot; 1/4 cup red wine; 6-ounces tomato paste; 28-ounces diced canned tomatoes; 1 tablespoon fresh chopped rosemary (or 1.5 tablespoons dried); 1 tablespoon fresh chopped thyme (or 1.5 tablespoons dried); 2 tablespoons hot pepper paste; 1 tablespoon lemon zest; 1 14-ounce can chickpeas or white beans; sea salt, black pepper; 1 cup grated Parmesan, seperated; 1/4 cup pesto; 4 eggs; pita or toast, for serving