To kick things off, start with the sauce. In a small saucepan, combine the dry white wine, white wine vinegar, bay leaf, shallot, and whole black peppercorns. Bring it to a boil over medium-high heat.

Lower the heat to a simmer until the mixture reduces to about one-quarter cup. This should take roughly 10-15 minutes. Make sure to stir occasionally to prevent burning. Once done, strain it through a fine mesh sieve, discarding the solids. Return the liquid to the pan and keep it warm.

In a mixing bowl, combine the reduction with the reserved tarragon stems, then add two egg yolks. Place the bowl over a pot of simmering water (this is a makeshift double boiler) and whisk constantly.

You want to be patient here; the stirring allows the eggs to cook gently without scrambling. Once the mixture thickens and doubles in volume, slowly drizzle in melted butter while continuing to whisk. Remember to whisk in the chopped tarragon for that burst of flavor.

While working on the sauce, preheat your oven to 400°F (200°C). Season the filet mignon generously with kosher salt and freshly cracked black pepper. Heat a cast-iron skillet over high heat, then add the olive oil.

Once it shimmers, place the steaks in the pan. Sear both sides for about 3-4 minutes until a golden crust forms.

Transfer the skillet to the preheated oven, cooking for an additional 5-8 minutes, depending on your desired level of doneness. I recommend using a meat thermometer for accuracy—130°F (54°C) for medium-rare.

Remove the skillet from the oven and let the steaks rest for at least 5 minutes. This allows the juices to redistribute, ensuring that the meat remains tender and moist.

Plate your filet mignon and generously spoon the Béarnaise sauce over the top. Serve alongside your favorite sides, and you’ve got an impressive meal ready to enjoy.