Combine eggplant, red and yellow bell peppers, garlic cloves, and onion on a sheet pan. Drizzle with olive oil and season with salt and pepper. Add 4 sprigs of thyme and 2 sprigs of rosemary.
On a separate sheet pan, combine the zucchini and yellow squash. Drizzle with olive oil and season with salt and pepper. Add 4 sprigs of thyme and 2 sprigs of rosemary.
Place the sheet pans in the oven and roast for 40 minutes. Stir the vegetables a few times while roasting and transfer the bottom pan to the top rack and the top pan to the bottom rack once during the cooking process for more even cooking.
Add the cherry tomatoes to the baking sheet with the bell peppers and eggplant and continue to roast for 20 minutes until the tomatoes burst and the squash and zucchini are fully golden and caramelized.
Combine the zucchini and squash on the baking sheet with the tomatoes, eggplant and peppers. Remove the thyme and rosemary sprigs. Toss with 2 tablespoons of balsamic vinegar and a drizzle of olive oil. Sprinkle with feta cheese and add the green olives. Roast for another 5 minutes until the olives are warm and the feta cheese is golden and melted.
Transfer to a serving platter and serve with freshly squeezed lemon juice and fresh basil.