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.
Notes
Substituions:
You can make this recipe vegetarian by substituting vegetable broth for chicken stock.
You could also make this recipe gluten free by substituting corn starch for the flour! Just make sure you add the corn starch at the very end rather than when the flour is added.
Don't have fresh thyme? Don't worry! You can use an 1/8 teaspoon dried.
Expert Tips:
If you don't have a stick blender, you can use a traditional blender. Just be careful! The soup will be very hot.