To begin, preheat your oven to 425 degrees F (220 degrees C). Then, prepare the beef tenderloin you will be using. Spread the beef with two tablespoons of softened butter after placing it in a small baking dish. Slide this into the oven, and allow it to bake until it is browned – this should take around 10 to 15 minutes. Once it is done, take it out, remove the beef from the dish, and put it aside, to allow it to cool. Reserve the leftover juices in the baking dish.
Now, take a small bowl, and add in the liver pate and 2 tablespoons softened butter – sprinkle in salt and pepper to taste, and mix it all together until it is completely blended, and creamy in texture. Spread this mixture all over the beef.
Then, place a small skillet on the stove over medium heat, and toss in the onions along with 2 tablespoons of butter. Sauté the onions until they become soft, and turn opaque in colour. Once they are done, take them out of the pan, allow them to cool, and then spread them over the pate-covered beef tenderloin.
Now, clear some space on a counter-top – make sure it is completely clean, dry, and clutter free – and roll out your puff pastry dough on this. Then, place the beef in the centre of this, and bring all the edges together, to fold and wrap the beef up in the pastry completely. Seal all the edges, making sure there are no fat, unsightly seams in the wrapped up pastry dough, and then trim any odd bits or extras off with a knife.
Slice a couple of slits in the top of the beef, and then place it in a 9x13 inch baking dish. Brush the top with some beaten egg yolk, and slide this into the oven to bake for 10 minutes at 450 degrees F (230 degrees C), and then for 10 to 15 more minutes at 425 degrees F (220 degrees C). You will know the dish is done when the top of the pastry develops a rich, golden brown colour. Once it is done, take it out of the oven, and put it aside to rest (make sure you keep it warm though).
While the Beef Wellington is resting, you will have just enough time to prepare a sauce to serve with it. Place a small saucepan on the stove, and pour in the beef stock, red wine, and the beef juices you reserved earlier. Boil it all together for 10 to 15 minutes until it reduces, and then strain it. Pour it into a sauce boat, and serve with sliced Beef Wellington.