In a pot, melt together your butter and olive oil. Toss in the cauliflower pieces and cook to brown - about 4 minutes, stirring occasionally. Next stir in the garlic for 30 seconds. Now pour in the broth, your seasonings and bring to a boil. Lower the heat to a simmer and cook for 6-7 minutes or until the cauliflower is fork tender.
Transfer the mixture to your food processor (you may have to work in batches) and pulse until a smooth consistency is reached; will take a few minutes.
Add the grated cheese into the food processor and pulse again until incorporated. Pour the sauce over the pasta and toss to coat. Serve with fresh chives and black pepper.