Preheat the oven to 400ºF. Trim the brussels sprouts by cutting off the stem end and removing any dead or browned outer leaves. Cut the sprouts in half. Peel the carrots and cut into 1-inch chunks.
Spread the trimmed sprouts and carrots out on a sheet pan and toss with the olive oil, salt, and pepper until well-coated. Put the pan in the preheated oven and roast for 10 minutes, or until the vegetables just begin to brown.
After 10 minutes, remove the vegetables from the oven. Sprinkle the chopped garlic over the vegetables and drizzle 2 Tablespoons of the honey over them. Toss to combine. Return the pan to the oven and roast another 8 to 10 minutes, or until the vegetables are golden brown and garlic has browned just a little. Remove from the oven, drizzle the last Tablespoon of honey over the vegetables and serve immediately.
Serving Size 1/4 cup