Combine celery and chicken broth in a small saucepan over very low heat; poach the celery for 20 minutes. Drain and cool. Combine celery with remaining ingredients except the butter, mixing well with your hands. Gently shape into 4 large patties, being careful not to compact the meat any more than necessary. Heat the butter in a large, heavy skillet over moderate heat until the butter is amber in color. Brown the burgers 6 minutes on each side, then place the skillet in a preheated 350F oven for 6 to 8 minutes for medium rare, a few additional minutes for better done.