In a large sauté pan, melt butter over medium low heat. Add shallots, garlic, and scallions to pan. Sauté for 5 minutes, stirring occasionally. Vegetables should be soft. Remove the vegetables with the butter from the pan. Set to the side and let cool.
In a large bowl combine ground beef, cooled vegetables with the melted butter, breadcrumbs, parmesan, beaten eggs, Worcestershire, salt and pepper. Gently mix with your hands.
Form into 4 oblong balls. Flatten to ½ inch thick. Make sure the sides of your patties are tight. Set to the side on a baking sheet.
Reheat the large sauté pan you used for the vegetables over medium heat. Add a tablespoon of butter. Once the butter is melted and bubbling, add the patties. Sear for 2 minutes on the first side.
Flip and sear for an additional minute. Remove patties and set them to the side on the baking sheet.