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Step 1
Drain the fat, but don't clean the pan: While your steaks are resting, pour off the fat from cooking and any aromatics that were cooked with the steak, but do not wipe the pan clean.
Step 2
Cook the shallot and thyme: Return the pan to medium heat and add the shallot and thyme and cook until fragrant and the shallot has softened.
Step 3
Deglaze the pan: Add the wine or broth and scrape the browned bits off the bottom of the pan with a wooden spoon or whisk. Cook until the liquid reduces slightly, about 1 minute.
Step 4
Add the mustard and butter: Whisk in the mustard and remove the pan from the heat. Vigorously whisk in the cold butter until thickened.
Step 5
Serve: Slice the steak and serve with the pan sauce.