In a small saute pan, over high heat, saute the shallots in the butter until soft, about 5 minutes. Divide the meat into 4 portions. One at a time, flatten each by chopping and spreading the meat with light strokes of your chefs knife. Season each with salt, pepper and 1/2 teaspoon of the shallots. Blend into the meat, chopping and turning it as you shape the portions into 4 1/2 to 5-inch round patties, 1/4-inch thick.
Toast the hamburger buns and distribute them to your guests. Suggest that they dress the bottom halves of their rolls as they wish while you cook the burgers.
Lightly dust the surface of a large, hot saute pan, with salt. When the pan is very hot, but not smoking, lay a patty in the pan. Rapidly add a second burger. Brown the meat, about 20 seconds. Turn patties to other side. Cook until done, about 1 minute. Remove cooked burgers to a warm platter. Repeat process with 2 remaining burgers. Place finished burgers onto guests buns as quickly as possible so they can add their finishing touches.