[From Good Housekeeping's Book of Menus, Recipes, and Household Discoveries (1922) p. 149-150]

               BROILED HAMBURG STEAK

1 1/2 pounds ground beef       1 tablespoonful butter
1 1/8 teaspoonfuls salt           1 tablespoonful minced parsley
1/4 teaspoonful black pepper  1 tablespoonful lemon-juice
                              Few grains paprika

Select round or flank steak and have it ground with two
ounces of suet.  Season with one teaspoonful of salt and the
pepper.  Mix it well, then place it on a meat board and gently
and lightly form it into an oblong cake about an inch thick.
Heat the broiler very hot and rub it over well with a piece of
suet, then place the meat cake on the hot bars and broil for
twelve minutes, turning once, using a broad spatula or pan-
cake turner.  Serve the steak on a hot platter with maitre
d'hotel butter rubbed over it.  To make this butter, blend to-
gether the butter, parsley, and lemon-juice, adding the latter
gradually, and season with one-eighth teaspoonful of salt and
the paprika.  Accompany with French-fried potatoes.

[notes: Most pre-ground beef today has enough fat that adding suet is not a good idea.
 Instead of broiling it on the oven rack, a cake-cooling rack over a pan to catch the drippings (or a pan with a built-in rack) is much easier to clean
 In a 1934 book there's a very similar recipe with no sauce, simply seasoned with salt and pepper and garnished with parsley. You can, of course also, broil individual hamburgers this way; they're much less greasy than when fried. It's interesting to note that in the books I've seen from this era, there is no mention of fried hamburgers.]