Melt the butter in a 12-inch skillet over medium heat; add the mushrooms, shallot, thyme, and 1/4 teaspoon salt.

Cook, stirring often, for 10–12 minutes, until the mushrooms release their liquid and the pan is dry, then spread the mixture on a plate to cool completely.

Cut the beef into 32 roughly 1-inch cubes, pat dry, and season with the remaining 1 teaspoon salt and the black pepper.

Heat the olive oil in the skillet over medium-high heat until shimmering.

Sear the beef in batches, turning to brown all sides, about 2–3 minutes per batch; transfer to a plate.

Refrigerate the beef for 15–20 minutes, until cool.

Heat the oven to 425°F and position racks in the upper and lower thirds; line two 18x13-inch rimmed baking sheets with parchment paper.

Roll each cold pastry sheet between parchment into a 9-inch square and cut each into 16 squares, each 2 1/4 inches wide.

Brush each beef cube with Dijon mustard.

Place about 1/2 teaspoon mushroom filling and one beef cube in the center of each pastry square, bring the corners up over the filling, and pinch to seal; arrange seam-side up on the baking sheets.

Beat the egg with the water and brush it over the exposed pastry.

Bake for 16–20 minutes, swapping the pans’ rack positions and rotating them front to back halfway through, until the pastry is deep golden and the centers of several beef bites reach 145°F on an instant-read thermometer.

Rest for 3 minutes before serving.