Preheat broiler. Place red pepper and garlic on a small baking sheet. Drizzle with a light large of olive oil and sprinkle with salt and pepper. Grill under the broiler until the skin is blackened, and the flesh has softened slightly, about 3-5 minutes.
While the red pepper is roasting, add onion and 1 tablespoon oil to a large heavy duty pan. Cook onion until it begins to turn golden brown. Add roasted red pepper and whole garlic. Cook for 2-3 minutes. Pour onion, red pepper, and garlic mixture into a blender along with the basil and salt + pepper to taste.
Return puree to skillet, and reheat until it begins to bowl. Stir in the half-and-half and the parmesan cheese, and spiralized sweet potatoes. Simmer for just 2-3 minutes. Turn off heat. Garnish with more parmesan cheese, and a drizzle of olive oil (optional).