Heat oven to 400°F. Toss prepped vegetables and garlic in the oil to coat.
Spread out on a large rimmed baking sheet, sprinkle with herbs, and generously season with salt and pepper.
Roast for 25 to 30 minutes, stirring occasionally until vegetables are crisp-tender and lightly browned in spots. Remove from oven, transfer to a serving bowl; shower with lemon juice and toss with cheese.
Vegetables can be prepared for roasting two or three days in advance and refrigerated until ready to use. Add even more interest to the dish by tossing in a handful of toasted pepitas or sunflower seeds.