Beef Wellington for Two

Adjust oven rack to upper-middle position and heat oven to 400 degrees. Line rimmed baking sheet with parchment paper. Pulse mushrooms in food processor until finely chopped, 13 to 15 pulses, scraping down sides of bowl as needed.

Pat filets dry with paper towels and season with salt and pepper. Heat oil in 10-inch nonstick skillet over medium-high heat until just smoking. Cook filets until well browned, about 2 minutes per side. Transfer filets to paper towel–lined plate.

Melt butter in now-empty skillet over medium-high heat. Add mushrooms, shallot, garlic, thyme, 1 teaspoon salt, and 1/4 teaspoon pepper and cook, stirring often, until browned and nearly all moisture has evaporated, 6 to 8 minutes. Stir in Madeira and cook until no liquid remains, about 2 minutes. Transfer to plate and let cool completely, about 20 minutes.

Roll puff pastry into 11-inch square on lightly floured counter. Cut pastry into 4 equal squares. Place 2 pastry squares on prepared sheet and spread 1/4 cup mushroom mixture in center of each, to about same diameter as filets, leaving 1-inch border. Place 1 filet on each mushroom-coated square. Spread ½ teaspoon mustard on top of each filet. Stretch remaining pastry squares over filets to meet bottom pastry squares. Cup your hands around filets to create tight shape.

Pinch top and bottom pastry squares together to seal. Trim excess pastry to form circle, leaving 1/2-inch border around filet. Crimp dough evenly around edge using your fingers. Refrigerate pastry packets, uncovered, until cold, about 1 hour.

Brush tops and sides of pastry packets with egg. Bake until meat registers 110 degrees, 18 to 20 minutes. Transfer sheet to wire rack and let packets rest, 10 minutes for medium-rare or 20 minutes for medium. (Puff pastry packets act as oven and continue to cook steaks while they rest.) Serve.