Gently mix the beef, egg, onion, cracker crumbs,
sage, 1/2 teaspoon salt and a few grinds of pepper in a large bowl using your
hands. Divide into 4 equal portions and shape into oval patties, about 1/2 inch
thick.
Heat 1 tablespoon butter in a large skillet over
medium-high heat. Brown the patties, about 4 minutes per side. Transfer to a
plate.
Add 1 tablespoon butter to the skillet and cook
the mushrooms until slightly browned, about 2 minutes. Stir in the
Worcestershire sauce, and salt and pepper to taste, scraping up any browned
bits. Sprinkle in the flour and stir, then stir in 2 1/2 cups hot water and
simmer until the sauce begins to thicken, about 2 minutes. Add the remaining 1
tablespoon butter, swirling to combine.
Return the patties and any juices from the plate
to the skillet. Simmer until the sauce thickens and the patties are cooked
through, about 2 minutes. Sprinkle with parsley and season with salt and
pepper. Serve with noodles, if desired.