In a large Dutch oven, cook bacon over medium heat, stirring occasionally, until crisp, about 8 minutes. Remove bacon using a slotted spoon, and let drain on paper towels, reserving drippings in pot.
Add onion to pot; cook until tender, about 5 minutes. Stir in garlic; cook until fragrant, about 1 minute. Add cauliflower, stock, thyme, salt, pepper, and nutmeg; bring to a simmer. Reduce heat to medium-low; cover and cook until vegetables are tender, 20 to 25 minutes. Discard thyme sprigs.
Working in batches, transfer soup to the container of a blender; blend until smooth. Return soup to Dutch oven; stir in milk and cheese. Garnish with bacon and thyme, if desired.