Place mushrooms in the bowl of a food processor. Blend to a very fine consistency.

Heat a frying pan over medium heat. Add mushrooms and 1 pinch salt and pepper. Cook until moisture evaporates and mixture thickens, about 5 minutes. Transfer to a plate.

Lightly season strip steak with salt and pepper. Heat a frying pan over high heat and add olive oil. Sear strip lightly on all sides to seal in juices, 5 to 7 minutes total, making sure not to overcook. Remove and baste with English mustard.

Lay out a large piece of plastic wrap and place prosciutto on top in 2 rows of 4, overlapping them. Spread mushrooms evenly on top. Place steak in the center and roll prosciutto tightly around it. Wrap tightly in plastic wrap, twisting the ends. Chill in the refrigerator for 20 minutes.

Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil.

Roll out pastry sheet; unwrap steak and place in the center. Mix egg and water in a bowl to make egg wash. Apply egg wash to the edges of the pastry using a pastry brush. Fold pastry tightly around steak. Chill for 5 minutes.

Brush egg wash over the pastry and sprinkle sea salt on top. Place on the prepared baking sheet.

Bake in the preheated oven until pastry turns golden, 25 to 30 minutes. Remove and let stand for 5 minutes before slicing into 1-inch pieces.