Heat oil in a large skillet over medium-high heat. Season filets with salt and pepper, then fry on each side until browned to lock in juices. Remove from the skillet and set aside to cool slightly.

Add mushrooms, wine, and beef consommé to the skillet; cook and stir over medium heat until mushrooms are tender. Use a slotted spoon to transfer mushrooms to a small bowl, reserving the consommé. Mix pâté with mushrooms, adding a little consommé if needed to achieve a spreadable texture. Divide mushrooms among filets and spread on the top. Refrigerate about 30 minutes.

Preheat the oven to 400 degrees F (200 degrees C). Lay puff pastry out on a clean surface and cut out two 5-inch rounds for each steak. Place a steak onto a round, and bring the edges up around the sides. Cover the top with a second piece of dough, overlapping the edges and pressing to seal into a package. Repeat with remaining steaks. Place Wellingtons onto a baking sheet, and brush the tops with beaten egg.

Bake for about 12 minutes, for rare, 16 minutes for medium, or 20 minutes for well done. For best results use a meat thermometer to determine the temperature of the steaks, with 140 degrees F (60 degrees C) being medium doneness. Remove from the oven and allow to rest for about 5 minutes.

While steaks are cooking, make sauce. Melt butter in a saucepan over medium heat. Stir in flour and cook, stirring constantly, until browned. Stir in green onions, and cook until tender, about 1 minute. Gradually stir in reserved consommé and remaining 1 cup of consommé; continue to cook and stir until sauce thickens. Reduce heat to low and stir in wine. Continue to simmer until thickened, about 15 minutes. Remove from the heat and stir in butter and parsley. Season with salt and pepper to taste.