In a large roasting pan (or on a rimmed baking sheet), combine the cauliflower, onion,and garlic. Drizzle the olive oil over and toss to coat.
Roast, stirring after 15 minutes, until the vegetables begin to brown and soften, for 30 minutes.
In a large saucepan, combine the cauliflower mixture with the chicken broth, water, bay leaf, and thyme. Cover and bring to a boil. Reduce the heat to a simmer. Simmer, still covered, until the cauliflower is tender, 20 minutes.
Discard the bay leaf. Transfer the soup to a blender or food processor, in batches, and puree until smooth.
Return the soup to a saucepan. Stir in the half-and-half. Season with salt and pepper, heat gently, and serve.