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Step 1
For the Herb Butter: Place all ingredients in a food processor and process until smooth. Spoon onto a piece of plastic wrap and roll into a log shape. Chill until firm.
Step 2
Fill a pot or other large container half full of hot or warm water. Preheat sous vide immersion cooker to 130° Fahrenheit. Vacuum seal filet mignon in a plastic bag using a vacuum sealer or water displacement method (see Notes). Place bag in water bath.
Step 3
Cook at least 1 hour (for 1-inch thick filet mignon), and no more than 4 hours (for 2.5-inch thick filet mignon).
Step 4
Remove filet mignon from bag and pat very dry. Season with salt and pepper.
Step 5
Heat cast iron skillet over medium heat for 3 to 5 minutes. Add butter, then immediately add steaks. Cook 2 minutes, then flip and cook another 2 minutes. Make sure steaks are coated in butter on each side in order to caramelize the exterior.
Step 6
When browned on both sides, plate and top with herb butter.