Place the celery and chicken broth in a small saucepan over very low heat. Poach the celery for 20 minutes. Drain and let cool.

In a mixing bowl, combine the poached celery with the ground beef, breadcrumbs, Worcestershire sauce, nutmeg, salt, and pepper. Mix well with your hands. Gently shape the mixture into 4 large patties, being careful not to compact the meat any more than necessary.

Preheat the oven to 350°F.

Heat the butter in a large, heavy skillet over medium heat until the butter is amber in color. Brown the burgers for 6 minutes on each side. Then transfer the skillet to the preheated oven for 6 to 8 minutes for medium rare, adding a few additional minutes if you prefer your burgers cooked beyond medium rare.