4 (5-ounce) filet mignons, room temperature

2 tablespoons vegetable oil
1/4 cup Dijon mustard
1 tablespoon horseradish
2 tablespoons unsalted butter
8 ounces cremini
mushrooms, chopped fine
1 shallot, minced
1 tablespoon thyme leaves
2 tablespoons heavy cream
1 tablespoon soy sauce
2 sheets phyllo, cut in half
4 thin slices prosciutto
2 sheets puff pastry, cut in half
1 large egg, beaten
Salt and pepper to taste
Season filets with salt and pepper. In a medium skillet over medium-high, heat 2 tablespoons oil. Sear top and bottom of each filet, about 90 seconds per side. In a small bowl, stir together mustard and horseradish. Transfer filets to a plate, spread outside with mustard mixture, and chill.
In the same pan, melt butter. Add mushrooms and cook until they have turned dark brown, about 6 minutes. Add shallot and thyme and cook until shallot is soft, about 2 minutes. Stir in cream and soy sauce and cook until cream is reduced and just coats mushrooms, about 5 minutes. Season mixture lightly with salt and pepper, transfer to a bowl, and chill until cold.
Line a baking sheet with parchment. Lay one half sheet of phyllo on the parchment. Lay one slice of prosciutto in center and spread with one-fourth of the mushroom mixture. Place filet on top and fold phyllo over, then flip and tuck sides underneath.
Roll one half sheet of puff pastry into a square. Wrap pastry around filet, tucking in corners. Flip again to tuck edges under. Place on prepared pan. Repeat with remaining ingredients. Chill 30 minutes.
Heat oven to 425 F. Use a very sharp knife to score top of pastry, then brush with egg. Bake until thermometer inserted into the center reads 125 F for medium rare, about 25 minutes. Let stand 5 minutes before serving.