Place broken down pieces of cauliflower on a rimmed baking sheet. Pour 2 Tbsp Fennel Olive Oil and 1/4 tsp kosher salt over cauliflower. Toss to coat. Spread out cauliflower into an even layer and roast in oven (middle position) at 450°F for approximately 40 minutes or until browned and tender, turning halfway through. Remove when done and set aside. Reserve a few pieces to garnish dish when serving.
Chop onion and garlic and remove leaves from thyme. In a large Dutch oven, heat the remaining 2 Tbsp of Fennel Olive Oil over medium heat until shimmering. Add garlic and onions and sauté about 5 minutes. Add cauliflower to Dutch oven along with 1 cup of water, 4 cups of broth and thyme leaves. Let come to boil then reduce heat to medium low and simmer 12-15 minutes.
Remove from heat and stir in half-and-half or milk. Using stick blender, puree soup until smooth. If using blender, blend in batches and crock lid to let steam escape. Add more salt and pepper to taste.
Serve in bowls garnishing with cauliflower pieces, thyme springs, fresh cracked black pepper, and a healthy drizzle of Fennel Olive Oil.