Combine the celery and chicken broth in a small saucepan over very low heat and poach the celery for 20 minutes.
Drain the celery and cool.
Combine the celery with the 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 350° F oven for 6 to 8 minutes for medium rare, a few additional minutes for better done.
Makes: 4