To a large mixing bowl, add the olive oil, balsamic vinegar, garlic, and salt and pepper.
Add the Brussels sprouts and carrots to the bowl. Use your hands or kitchen tongs to toss well to coat the vegetables with the olive oil mixture.
Line a baking sheet with parchment paper for easier cleanup. Transfer the vegetables to the baking sheet and spread out in a single layer.
Bake for 25 minutes, tossing the vegetables with the kitchen tongs halfway though, or until the vegetables are browned on the outside and tender when pierced with a fork.
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Notes
Tip: If you are using your oven to cook something else at the same time at 400° or 425°, you can roast the vegetables at that temperature, too. They will take a little longer at the lower temperature, around 30 to 40 minutes. For best results, always roast veggies between 400° and 450°.Storing and freezing: Leftovers can be covered and refrigerated for up to 5 days and enjoyed cold or reheated in the microwave. Or freeze room temperature cooked vegetables in a glass container with a lid or a freezer bag for up to 9 months. You do not need to defrost them before reheating them.