Heat the olive oil in a medium skillet over medium-high heat. Add the zucchini and cook until just starting to soften, 5 to 7 minutes; using a slotted spoon, transfer to a paper towel-lined plate. Repeat with the eggplant, and then the red and yellow peppers (the peppers can be cooked together), adding more olive oil in between if the skillet seems dry. Set the vegetables aside.
In the same pan, saute the onions until just starting to soften, about 5 minutes. Add the garlic and cook until fragrant, about 2 minutes. Add the sauteed vegetables back to the pan as well as the tomato paste, parsley, thyme, bay leaf, tomatoes, 1 teaspoon salt and 1/2 teaspoon pepper. Stir to coat all the vegetables with the tomato paste. Cover and cook over low heat until the tomatoes have softened and the flavors have had a chance to meld, about 15 minutes. Taste the ratatouille and add salt or pepper as needed.
Remove and discard the bay leaf and the parsley and thyme sprigs. Sprinkle with the basil. Serve immediately.
To skin a tomato, score an "x" in the bottom of a tomato, then place in a pot of simmering water until you start to see the skin pull away at the edges, 20 to 40 seconds. Transfer the tomato to a bowl of ice water. You should be able to pull the skin off easily.