In her 1980’s series The Way To Cook Julia Child gave a recipe for hamburgers that included the following:

1 1/2 lbs ground chuck
1 egg
2 T sour cream
1/8 – 1/4 t thyme or Italian seasoning
salt
fresh ground black pepper
2 T grated onion

Julia mixed the above ingredients, divided into 4 patties, lightly dredged them in flour and sautéed them in a fry pan with a tiny amount of oil. She served them on a toasted bun with lettuce and salsa.

For my Salisbury steak version:

Leave off the flour dredge and sauté until nearly done.

Remove the patties from the pan and sauté a few onions in the fat.  When the onions are starting to lightly caramelize, create a roux by stirring in about 2 tablespoons of flour. Cook the flour for a couple minutes and enough water to form a slightly too-thin brown gravy.

Add the undercooked beef patties to the brown gravy and simmer until the gravy has thickened, spooning the gravy over the patties several times.

Adjust seasonings and serve. The gravy may be enriched with a small dollop of sour cream, should you desire.