Begin by preheating the oven to 425 degrees Fahrenheit (220 degrees Celsius).

Position the beef tenderloin in a baking dish, then generously spread two tablespoons of softened butter over the top.

Bake the beef in the preheated oven until it achieves a golden brown color, approximately 10 to 15 minutes. Once done, remove the beef from the pan, reserving the juices, and allow it to cool completely.

Increase the oven temperature to 450 degrees Fahrenheit (230 degrees Celsius).

In a skillet, melt two tablespoons of butter over medium heat. Add the chopped onion and sliced mushrooms, sautéing them for about five minutes until softened. Remove the skillet from the heat and let the mixture cool.

In a bowl, combine the liver pâté with the remaining two tablespoons of softened butter, seasoning with salt and pepper. Spread this mixture evenly over the cooled beef tenderloin. Top with the cooled onion and mushroom blend.

Roll out the thawed puff pastry to a thickness of about 1/4 inch, then place the beef in the center of the pastry.

Fold the pastry over the beef, sealing all edges securely, ensuring the seams are not overly thick. Transfer the wrapped beef to a 9x13-inch baking dish. Cut several slits in the top of the pastry and brush with the beaten egg yolk.

Bake the Wellington in the preheated oven for 10 minutes. After this time, reduce the heat to 425 degrees Fahrenheit (220 degrees Celsius) and continue baking until the pastry turns a rich, golden brown, approximately 10 to 15 minutes more. An instant-read thermometer inserted into the center should register between 122 to 130 degrees Fahrenheit (50 to 54 degrees Celsius) for medium-rare. Allow the dish to rest once out of the oven.

Meanwhile, place the reserved pan juices in a small saucepan over high heat. Stir in the beef broth and red wine, boiling the mixture until it slightly reduces, about five minutes. Strain the sauce and set aside to serve with the beef.

Serve the Beef Wellington hot and enjoy!