1. Put olive oil in a bowl and toss the carrots and cauliflower in it. Add salt and pepper Put them on a baking sheet and bake at 425?F for 30-35 minutes. Flipping halfway in between.
2. Put about 2 tablespoons of olive oil and heat until shimmering. Add the garlic and onion, sautéing until the onions are soft..about 8 minutes. Add the cauliflower and carrots. Add the broth and bring to a boil. Bring back down to a simmer for about 10 minutes.
3. Let the soup cool, then puree the mixture in halves, letting the steam release by putting a cloth where the plastic stopper would otherwise be.
4. Bring the soup back to a simmer, stir in half and half, basil, and cheese.