Heat the olive oil in a skillet over medium heat. Add the mushrooms and onion and cook, stirring often, until their moisture has evaporated and the vegetables are softened, about 8 to 10 minutes. Stir in the garlic and thyme, cook for 30 seconds, then transfer the mixture to a plate to cool.

Heat the oven to 400°F. In a mixing bowl, combine the ground turkey, ground beef, breadcrumbs, salt, pepper, and half of the egg, lightly beaten. Add the cooled mushroom mixture and mix just until combined.

Shape the meat mixture into a compact loaf on a parchment-lined baking sheet. Bake for 25 minutes, then remove it from the oven and let it cool until no longer steaming. Keep the oven on.

Unfold the thawed puff pastry on a lightly floured surface. Roll it out just enough to fit around the loaf. Spread the Dijon mustard over the top and sides of the cooled meatloaf, then place it in the center of the pastry.

Fold the pastry over the meatloaf, trimming any excess if needed. Pinch the seams closed and place the loaf seam-side down on the baking sheet. Beat the remaining egg and brush it over the pastry.

Bake for 25 to 30 minutes, until the pastry is deeply golden and crisp and the center of the meatloaf reaches 165°F. Rest for 10 minutes before slicing so the filling holds together.