Heat the Oven: Preheat to 180°C/350°F. Use an oven-safe Dutch oven or transfer to an oven-safe baking dish before baking the eggs.
Aromatic Sweat (8–10 minutes): Warm the olive oil over low–medium heat. Add onions and 2 tablespoons water, cover, and sweat until translucent, stirring occasionally. Stir in the garlic and cook 1 minute.
Pepper Sizzle & Steam (6–8 minutes): Add bell peppers. Cover 3 minutes to steam, then uncover and cook 3–5 minutes more over medium heat. If browning threatens, splash in a tablespoon of water and scrape up any fond.
Herb & Paprika Bloom (30 seconds): Stir in smoked paprika, oregano, thyme, and bay leaves until fragrant.
Zucchini–Eggplant Softening (8–10 minutes): Add zucchini and eggplant with black pepper (and a tiny pinch of salt if using). Cover to trap steam; stir occasionally, using small splashes of water instead of more oil to prevent sticking.
Tomato Melt & Chickpea Silk (15–20 minutes): Add tomatoes and bring to a lively simmer. Stir in the chickpea purée until fully dissolved. Simmer gently, uncovered, stirring every few minutes, until vegetables are tender and glossy. Off the heat, stir in the sherry vinegar and lemon zest.
Nest & Bake the Eggs (7–10 minutes): Make six shallow wells. Crack one egg into each. Transfer to the oven and bake uncovered until whites are just set and yolks are still soft, 7–10 minutes.
Green Finish (30 seconds): Remove bay leaves. Scatter parsley over the top.
Rest & Serve (3 minutes): Let the pan rest off heat briefly for gentle carryover cooking. Serve straight from the pan.