In a medium stockpot, melt butter.
Add onion, celery, and garlic.
Cook over medium heat until translucent, about 10 minutes.
Stir in flour and then chicken broth.
Add milk, cream, and thyme.
Puree with a stick blender (or a traditional blender, in small batches).
Cook over medium low heat for 15-20 minutes, stirring frequently.
Season with salt and pepper.