Melt the butter in a Dutch oven over medium-high heat. Add the onion and garlic; cook, stirring, until they start softening, about 4 minutes.
Add the cauliflower, thyme, salt and pepper. Cook, stirring, until the cauliflower starts browning, 5 minutes.
Stir in the flour until absorbed, about 1 minute. Add the chicken broth and milk; bring to a boil. Reduce the heat; simmer until the cauliflower is tender, 25 - 30 minutes.
Use an immersion blender to puree soup until smooth or, working in batches, transfer the soup to a blender and puree.
Return the soup to the pot over medium heat. Stir in the cheese until melted; add up to 1 cup water if the soup is too thick.
Stir in the cooked pasta. Serve with more fresh thyme.
