Melt together the olive oil and butter in a large dutch oven over medium heat. Add the onion and carrots and cook until fragrant, about 10 minutes. Stir in the flour and cook until golden, about 2 minutes, then gradually whisk in the broth. Add the cauliflower and bring to a boil. Cover, and cook over medium heat for 10 minutes, until the cauliflower is tender. Transfer the soup to a blender and purée until smooth. Return the soup to the pot. If needed add 1-2 cups water, then the broccoli, bay leaves, paprika, cayenne, and a large pinch each of salt and pepper. Bring to a simmer over medium heat and cook, uncovered, until the broccoli is tender, about 10 minutes.Remove the bay leaves and blend the soup in batches until the broccoli is finely chopped, but small chunks still remain. Return the soup to the stove and set over low heat. Stir in the coconut milk and cheese until melted and creamy. Taste, and add salt and pepper as needed. Ladle into bowls and top with a little extra cheddar and fresh thyme. Enjoy!