Add serious class and flavor to a filet mignon with a classic French Bearnaise sauce that never goes out of style. Bearnaise sauce and filet mignon are a match made in heaven paired with hearty veggies like potatoes and grilled mushrooms. The sauce is an emulsification — egg yolks and butter whisked with vinegar flavored with tarragon and shallots, with a bite of black and cayenne pepper. The sauce requires plenty of whisking and a careful hand. Once poured over the steak, this sauce adds rich flavor to an already perfectly cooked cut of meat.