Heat olive oil in a large pan over medium heat. Cook and stir onion and garlic in hot oil until tender, about 5 minutes.
Stir tomato passata, red wine, parsley, basil, oregano, salt, pepper, bay leaf and chilli flakes with the onion and garlic; bring to a simmer, reduce heat to low and cook until the sauce has thickened, about 45 minutes.
Crack eggs into a bowl one at a time and gently slide them into the tomato sauce; cook until beginning to firm, 2 to 3 minutes. Spoon sauce over the eggs to cover. Place a lid on the pan and simmer until sauce has thickened, about 30 minutes.