Heat the oven to 425°F. Toss cauliflower, carrots and onion with olive oil, salt, pepper and thyme on an 18-by-13-inch rimmed sheet pan.
Spread vegetables in one layer with flat sides against the pan and roast for 12 minutes.
Turn the vegetables and add sausage rounds, distributing them across the open spaces. Roast for 15 minutes more.
Stir Dijon and cider vinegar together in a small bowl. Drizzle over the tray, toss gently and roast for 3 to 5 minutes until the carrots are tender and the sausage is hot throughout.
Divide sausage and vegetables evenly among 4 plates, scraping up the browned bits without adding extra liquid.