In an extra-large skillet cook onion, celery in with 1 Tbsp. of butter for 6 minutes or until tender; transfer to a food processor.
In the same skillet cook mushrooms with 2 Tbsp. butter for 12 minutes or until browned and all liquid has evaporated.
In a food processor or blender combine the onion, celery, half the mushrooms, and 3/4 cup of the chicken broth. Cover and process or blend until smooth; set aside
In a medium saucepan melt 1 Tbsp. butter. Stir in flour, thyme, salt, and pepper. Add 1 cup milk all at once. Cook and stir until slightly thickened and bubbly. Cook and stir 1 minute more.
Stir in the reserved mushrooms, blended vegetable mixture, and the remaining 3/4 cup broth. Cook and stir until heated through. If necessary, stir in additional milk to reach desired consistency. Season to taste with additional salt and pepper.