Finely chop the mushrooms. Heat a dry skillet over medium heat and cook the mushrooms until all moisture has evaporated (about 8-10 minutes) to create the duxelles. Season with salt and pepper, then set aside to cool.

Season the filet mignon steaks generously with salt and pepper. Heat olive oil in a skillet over high heat. Sear the steaks for 1-2 minutes per side to develop a crust. Remove from heat, brush immediately with Dijon mustard, and let rest until completely cool.

Roll out the puff pastry and cut it into two equal squares. Spread half of the cooled mushroom duxelles in the center of each pastry square.

Place a cooled, seared filet mignon on top of the duxelles. Fold the pastry edges over the beef to completely encase it, trimming any excess pastry. Pinch the seams to seal.

Place the wrapped beef seam-side down on a parchment-lined baking sheet. Chill in the refrigerator for at least 30 minutes to firm up the pastry.

Preheat the oven to 400 degrees Fahrenheit (200 degrees Celsius). Brush the chilled puff pastry with the beaten egg wash. Bake for 20-25 minutes until the pastry is golden brown and a meat thermometer reads 130 degrees Fahrenheit for medium-rare.

While the Wellingtons bake, boil the cubed potatoes in salted water until fork-tender. Drain and return to the pot. Mash with 3 tablespoons of butter and heavy cream until smooth. Stir in chopped chives.

Steam the green peas until tender, and toss with the remaining 1 tablespoon of butter.

Remove the Beef Wellingtons from the oven and let them rest for 10 minutes before serving. Serve whole alongside the creamy mashed potatoes and buttered peas.