Clean and dice all the vegetables, onions, and garlic, removing the seeds from the eggplants and bell peppers.
In a dutch pan or large saucepan, confit (cook slowly in oil) the eggplants in ½ cup of olive oil. Eggplants retain a lot of oil, so you need to nourish them well from the start. Once the eggplant starts to moisten, add the bell peppers, followed a few minutes later by the onions, bay leaves, rosemary, and garlic, stirring regularly and enjoying the perfumes from the south of France.
Add the tomatoes and the rest of the olive oil. Cover the pot and let cook for 15 minutes. Add the zucchini and cook for ten more minutes, and at the last moment, add some fresh basil. Salt and pepper to your taste.
Bring 1.5 L of water to boil in a large saucepan.
Lower the heat to a simmer (you don’t want big boiling bubbles).
Break one egg in a small bowl. In the saucepan, use a fork to stir the water in a spiral movement. Add the white vinegar and salt. Gently pour the egg into the water and use a spoon to hold the egg white around the egg yolk.
Cook for about 2 minutes. The egg should be soft, and the white should be cooked.
Remove the egg from the saucepan and cool it off quickly in a bowl of cold water. Take the egg out of the water and place it on a tray with a paper towel.
Salt with a pinch of fleur de sel.
Repeat with the other eggs.
Serve the warm ratatouille with a poached egg.