Set the oven to 400°F and cover a sheet pan with parchment paper. The lined surface will help you lift the baked parcels without tearing their undersides.
Season the beef with kosher salt and pepper, then heat the butter and olive oil in a large skillet over medium-high heat. Wait until the butter has melted and the fat is hot enough for the meat to sizzle on contact.
Sear the beef for about 45 seconds per side, then transfer it out of the skillet to partially cool. Look for a browned exterior rather than a cooked-through center, since the meat still has an oven bake ahead.
Pulse the mushrooms into fine pieces, then cook the onion and thyme in the skillet drippings over medium heat for 5 minutes. The onion should look translucent and the thyme should smell fragrant.
Stir the chopped mushrooms into the skillet and cook for 8 to 10 minutes, stirring as needed, then take the pan off the heat and mix in the Dijon mustard. The filling is ready when the mushrooms look golden and no liquid remains pooled in the pan.
On a lightly floured surface, roll one pastry sheet into a 10-inch square, cut along its folds into 3 strips, and halve each strip crosswise; repeat with the second sheet. You should have 12 pastry pieces with enough room to enclose the filling.
Center about 2 teaspoons of mushroom filling on each pastry piece and add a piece of beef. Keep the borders clear, and make sure the filling no longer feels hot enough to soften the dough.
Coat the pastry borders with beaten egg white, bring the dough around the filling, press the edges closed, and arrange each parcel with its seam underneath on the prepared pan. The joins should hold together without gaps or exposed filling.
Brush the tops with beaten egg yolk, scatter over the sea salt flakes, and bake for 16 to 18 minutes until golden. Look for puffed layers and deeply colored edges, while checking the beef separately for doneness.
Let the parcels cool slightly, then finish with chopped parsley and serve with the bottled horseradish cream sauce. The pastry should remain crisp while the filling becomes easier to handle.