In a large pot, melt butter over medium heat. Add diced onion and garlic, sautéing until fragrant and translucent, about 3 minutes.
Add the chopped cauliflower to the pot and pour in the broth. Bring to a boil, then reduce the heat and let it simmer for about 20 minutes or until the cauliflower is soft.
Use an immersion blender to puree the soup until smooth and creamy. If using a regular blender, blend in batches, then return the soup to the pot.
Stir in the heavy cream, salt, black pepper, and thyme. Let the soup simmer for another 5 minutes to enhance the flavors. For extra richness, stir in shredded cheddar cheese.
Ladle the soup into bowls and garnish with extra cheese, fresh herbs, or crispy bacon bits. Pair it with Cheesy Mashed Potato Puffs for a hearty meal!