Gather your ingredients and preheat the oven to 400°F/200°C.
Peel and dice the carrots and cut the brussel sprouts into halves.
Add the vegetables to a large roasting pan or sheet pan. Drizzle over the olive oil and add the smashed garlic, a few rosemary sprigs and some salt and pepper to taste. Toss well.
Roast for 45-50 minutes, until the veggies are tender and starting to brown.
A drizzle of maple syrup or honey added before or after roasting can add a bit of sweetness to this dish.
Feel free to experiment with other herbs too, such as thyme or sage.
Your brussel sprouts may take more or less time to cook, depending on the size of the sprouts, the size of the pan, and how well-done you like them. Keep an eye on them while they cook.
If your veggies are browning too quickly, cover the pan with foil and continue cooking until they are tender, but not burnt.