Prepare the vegetables — Cut eggplants, zucchinis, peppers, onion, and tomatoes into medium chunks so they cook evenly and keep some shape.
Heat the olive oil — Warm the oil in a large pan over medium heat until it looks shiny and fluid but not smoking.
Cook the onion first — Add the onion and cook until soft and slightly golden, stirring occasionally, until it smells sweet and mellow.
Add garlic and peppers — Stir in the garlic and bell peppers and cook until the peppers begin to soften and release a light aroma.
Cook the eggplant — Add the eggplant and stir well so it absorbs some oil. Cook until it starts to look glossy and slightly soft.
Add zucchini and tomatoes — Stir in zucchini and chopped tomatoes. The mixture will look juicy at first, which is normal.
Season the dish — Add salt, pepper, thyme, and rosemary, then stir to distribute the herbs evenly.
Simmer slowly — Cook uncovered on low heat, stirring occasionally, until the vegetables are tender and the liquid thickens into a light sauce.
Finish with basil — Turn off the heat and add fresh basil leaves. Let the dish sit a few minutes before serving so the flavors settle.