Cut the eggplant into 3/4-inch (2 cm) cubes and place them in a colander set over a bowl or in the sink.
Sprinkle generously with salt and toss to coat. Let them sit for 20 minutes while you prep the other vegetables.
You'll see beads of brown liquid form on the surface. Rinse quickly under cold water if you're watching sodium, then blot the cubes very dry with paper towels or a clean towel.
Cut the zucchini into 3/4-inch (2 cm) half-moons, keeping the pieces close in size to the eggplant so everything cooks at a similar rate.
Seed and dice the red and yellow bell peppers into 3/4-inch (2 cm) pieces. Dice the onion and mince or grate the garlic.
If using canned whole tomatoes, crush them by hand into a bowl, juices and all. If using fresh, chop them roughly.
Heat 2 tablespoons of the olive oil in a large skillet over medium-high heat until it shimmers.
Add the eggplant in a single layer, working in batches if needed to avoid crowding. Cook for 4 to 5 minutes, turning once or twice, until the cubes are golden and just tender.
Transfer the eggplant to a wire rack or a plate lined with paper towels.
Add another tablespoon of olive oil to the same skillet. Add the zucchini in a single layer and cook for 3 to 4 minutes, until lightly browned but still firm.
Set the zucchini aside with the eggplant. It should keep a slight bite at this stage, since it will finish cooking later.
Set your Dutch oven over medium heat and add the remaining olive oil, about 2 tablespoons. Stir in the herbes de Provence and let them bloom in the oil for 30 seconds until fragrant.
Add the diced onion and bell peppers with a pinch of salt. Cook for 8 to 10 minutes, stirring often, until soft and just starting to color.
Add the minced garlic and cook for 1 minute more, until aromatic but not browned.
Stir in the tomato paste and cook for 1 to 2 minutes, letting it darken slightly to deepen the flavor.
Add the crushed tomatoes and their juices, the bay leaf, 1 teaspoon of salt, and the black pepper. Bring to a gentle simmer and let the base cook uncovered for 10 minutes, stirring now and then, until it thickens slightly.
Return the browned eggplant and zucchini to the pot and fold them gently into the tomato base. Simmer uncovered for 20 to 25 minutes, stirring occasionally, until the vegetables are tender and the sauce coats them without pooling.
Keep the pot uncovered the whole time. Trapped steam is what makes the finished dish watery.
Remove and discard the bay leaf. Stir in the torn basil and the optional tablespoon of red wine vinegar. Taste and adjust the salt and pepper.
Let the ratatouille rest off the heat for at least 10 minutes before serving. It tastes even better after a rest, warm rather than piping hot.