Step 1: Prepare the Beef Fillet

1. Bring the Beef to Room Temperature:

Before cooking the beef tenderloin, take the fillets out of the refrigerator and let them sit at room temperature for about 20-30 minutes. This ensures even cooking.

2. Season the Beef:

Generously season each beef fillet with salt and freshly ground black pepper on both sides. Press the seasoning into the meat to ensure it adheres.

3. Preheat the Pan:

Heat a large cast-iron skillet or heavy-bottomed frying pan over medium-high heat. Add 2 tablespoons of olive oil and let it heat until shimmering.

Step 2: Sear and Cook the Beef Fillets

1. Sear the Beef:

Place the seasoned beef fillets in the hot pan and sear for about 3-4 minutes on each side, or until they develop a beautiful golden-brown crust. Use tongs to avoid piercing the meat, which can cause juices to escape.

2. Add Butter, Garlic, and Rosemary:

Reduce the heat to medium and add 2 tablespoons of unsalted butter, crushed garlic cloves, and rosemary sprigs to the pan. As the butter melts, use a spoon to baste the fillets with the flavorful butter for about 2 minutes. This adds extra flavor and richness to the beef.

3. Check for Doneness:

For medium-rare beef, cook the fillets until they reach an internal temperature of 130°F (54°C). For medium, cook until the internal temperature reaches 140°F (60°C). You can use a meat thermometer to check the doneness.

4. Rest the Beef:

Once the fillets are cooked to your desired doneness, transfer them to a plate and loosely cover with foil. Let the beef rest for about 5 minutes to allow the juices to redistribute.

Step 3: Make the Easy Béarnaise Sauce

1. Create the Reduction:

In a small saucepan, combine white wine vinegar, white wine, shallots, crushed peppercorns, and tarragon sprigs. Bring the mixture to a simmer over medium heat and cook until the liquid reduces by half, about 5 minutes. Strain the reduction into a small bowl and discard the solids. Set the reduction aside to cool slightly.

2. Whisk the Egg Yolks:

In a heatproof bowl, whisk the egg yolks together with the vinegar reduction until smooth. Place the bowl over a double boiler (a pot of simmering water) and continue to whisk the egg yolk mixture constantly.

3. Add the Butter:

While whisking, slowly drizzle in the melted butter a little at a time, ensuring the butter emulsifies with the yolks. The sauce will thicken as you add the butter. If it becomes too thick, you can add a teaspoon of warm water or lemon juice to thin it out slightly.

4. Finish the Béarnaise Sauce:

Once all the butter is incorporated, remove the sauce from the heat and stir in the chopped tarragon leaves. Season with salt to taste, and a squeeze of lemon juice if you prefer a tangier flavor.

Step 4: Serve the Beef Fillet with Béarnaise Sauce

1. Slice the Beef:

After the beef fillets have rested, slice them into thick medallions if desired, or serve them whole.

2. Drizzle with Béarnaise Sauce:

Generously spoon the warm Béarnaise sauce over the beef fillets, allowing it to cascade over the edges. The creamy sauce adds a delicious richness to the tender beef.

3. Garnish and Serve:

Garnish the dish with fresh sprigs of rosemary or a sprinkle of chopped tarragon for a pop of color. Serve immediately with your choice of sides.