Preheat oven to 400 degrees F.
In a large, oven-proof skillet, over medium heat, saute celery in 1 tablespoon butter, about 4 minutes. Remove celery and let cool.
Melt remaining butter in skillet. Carefully place patties in skillet and cook 2 to 3 minutes, or until browned on 1 side. Flip patties and place in preheated oven. Cook for 12 to 15 minutes for medium doneness.
Serve hot on toasted buns with desired condiments.