Summer Filet of Beef with Béarnaise Mayonnaise
6 tablespoons (¾ stick) unsalted butter, melted
Kosher salt and freshly ground black pepper
¾ cup minced shallots (3 shallots)
4 tablespoons minced fresh tarragon leaves, divided
½ cup dry white wine
¼ cup tarragon or white wine vinegar
2 extra-large egg yolks, at room temperature
2 tablespoons freshly squeezed lemon juice, at room temperature
1 tablespoon Dijon mustard
1 cup vegetable or canola oil, at room temperature
½ cup good olive oil, at room temperature
Preheat the oven to 400 degrees. Line a sheet pan with parchment. Dry the entire tenderloin with paper towels and brush it all over (top and bottom) with the butter. Sprinkle it all over with a generous amount of sea salt and freshly ground black pepper. Place the filet on the sheet pan and roast it for approximately 35 – 40 minutes, until an instant-read thermometer inserted into the center of the beef registers 120 degrees for medium rare. Remove from the oven, cover losely with aluminum foil, and allow to rest at room temperature for 15 minutes. Discard the foil and allow to sit at room temperature.
Meanwhile, place the shallots, 3 tablespoons of tarragon, the wine, and vinegar in a small saucepan and bring it to a boil over medium-high heat. Boil for 5 minutes, until only 1 tablespoon of liquid remains. Set aside to cool for 15 minutes.
Place the egg yolks, lemon juice, mustard, 2 ½ teaspoons salt, and 1 teaspoon pepper in the bowl of a food processor fitted with the steel blade and process for 10 seconds. With the processor running, slowly pour the vegetable oil and olive oil through the feed tube to make a thick emulsion. Add the shallot reduction and the remaining tablespoon of tarragon leaves and pulse to combine. Refrigerate until ready to serve.
Slice the filet of beef between ¼ and ½ inch thick, sprinkle with salt, and serve warm, at room temperature, or cold with the béarnaise mayonnaise on the side.