Preheat the oven to 450 F. Make sure you have one oven rack positioned in the bottom third of the oven and one on the top third. Line two rimmed baking sheets with parchment paper, if you have it. Either way, spray them with nonstick cooking spray.
Salt the eggplant: Place half of the cubed eggplant in a colander, and sprinkle it with ½ teaspoon kosher salt. Scatter the rest of the eggplant over, then sprinkle with another ½ teaspoon salt, then use your hand to quickly toss the salted eggplant. Leave it sit in the sink place or over a bowl to catch the liquid, for 20 minutes. Turn the eggplant onto a clean dishtowel or paper towels and blot until fairly dry.
While the eggplant is being salted, place the onions on half of one of the sheet pans, drizzle over 2 tablespoons of the olive oil, and toss to coat. Spread out on half the sheet pan. Add the red and orange bell pepper to the other side of the sheet pan. Drizzle the peppers with 2 more tablespoons of the oil, toss, and spread out to cover the second half of the sheet pan. Sprinkle with salt and pepper.
Do the same thing with the other sheet pan: On one half toss the blotted dry eggplant with 2 tablespoons olive oil, and on the other side, the zucchini and summer squash with 2 more tablespoons of olive oil on the other side. The vegetables should be a bit crowded, but still in a single layer. Sprinkle with salt and pepper.
Tuck the smashed garlic cloves, and sprigs of thyme and rosemary will nilly amongst the vegetables, distributing them evenly.
Roast the vegetables for 15 minutes, then remove the trays, and give each tray a good stir, trying to keep the vegetables on their own sides of the baking sheets. Shove the eggplant over towards the peppers so that it opens up about a third of the space on the sheet pan. Add the tomatoes, to the space, drizzle with the remaining tablespoon of oil, and give a quick salt and pepper sprinkle. Return the baking sheets to the oven, but switch which rack they are placed on. Roast for another 20 to 25 minutes, until all of the vegetables are tender and lightly browned in spots.
Let the vegetables cool for 5 minutes on the baking trays, then scrape them into a large bowl. Add the parsley and basil, and toss. Taste and adjust seasonings as needed.
Serve the ratatouille hot, warm, or at room temperature.
Notes
Some classic ratatouille recipes call for each vegetable to be cooked separately, and then combined all at the end. However, in the end, they are all coming together into one dish, so I don’t think we need to be too precious about cooking them vegetables together.
Salting the eggplant pulls out excess moisture and bitterness, but if you don't have the time, you can skip this step.