In a large nonstick skillet, heat 2 tablespoons olive oil over medium heat. Add the eggplant and cook, stirring, until golden, about 5 minutes. Add 2 tablespoons olive oil, the zucchini, onion, bell pepper and 1/4 teaspoon each salt and pepper and cook, stirring, until crisp-tender, about 6 minutes. Stir in the tomatoes and thyme, partially cover and cook until tender, about 5 minutes; season with salt and pepper. Simmer, uncovered, for 2 minutes more to cook off any liquid. Transfer to a large bowl and wipe the skillet clean.
Lay the wraps on a work surface. Sprinkle one-quarter of the cheese in the center of each wrap and top with 1 cup ratatouille. Fold burrito-style to enclose.
In the same skillet, heat 2 tablespoons olive oil over medium heat. Add 2 wraps, seam side down, and cook, turning once, until golden, about 4 minutes. Repeat with the remaining olive oil and wraps.