Position racks in the top and bottom thirds of the oven and heat the oven to 400 degrees F. Line two large rimmed baking sheets (12x16-inch sheet pans are a good size) with foil and top with a sheet of parchment. In a large bowl, toss the onions, peppers, eggplant, zucchini, garlic, olive oil, rosemary, and 1-1/2 teaspoons kosher salt. Spread the vegetables evenly over both sheets. Don't spread the vegetables too thin or they may burn (they shrink a lot as they cook).

Roast, stirring the vegetables a few times and swapping the positions of the pans once, until the vegetables are slightly collapsed or shriveled, starting to brown, and very tender, about 45 minutes. If the vegetables look like they may burn, turn down the heat or pile them closer together. If they look dry, drizzle on a little olive oil. Divide the tomatoes between the two pans and continue to roast until the tomatoes soften and shrink and the other vegetables are well-browned, another 30 to 50 minutes. Scrape all the vegetables and any juices into a serving bowl. Toss with the basil, taste for seasoning, and serve warm.