Preheat oven to 400 degrees F. Line two large baking sheets with parchment paper. Cut the backstrap into 1- to 2-inch cubes.
Cut the backstrap into 1- or 2-inch cubes.
Add the shallots and mushrooms to a food processor and pulse on high until both are finely minced and mixed well.
Heat oil in a large skillet over medium-high heat. Pat the venison chunks dry with paper towels. Season all over with salt and pepper. Add to skillet and sear on all sides, until browned, about 2 to 3 minutes. All you want to do on this step is brown the venison, it will continue to cook in the oven so don’t overdo it. Medium-rare backstrap will be better in the finished recipe. Remove from heat and wipe skillet with paper towel.
Season the backstrap with salt and pepper and brown in oil.
Melt butter in the same skillet over medium heat. Add mushrooms and shallots and sauté until tender. Season with salt and pepper. Stir in rosemary and remove from heat.
On a lightly floured surface, unfold puff pastry. Stack both sheets and roll into a large square, about 1/8-inch thick.
Roll out two sheets of puff pastry on a floured surface.
Cut each into 16 squares. Place one piece of meat onto each square and dollop with about a teaspoon of mustard. Top the meat with about a tablespoon of the mushroom mixture. Fold pastry edges over the meat and pinch to seal. Place on baking sheets and brush with egg wash. Bake 14 to 16 minutes or until golden-brown. Garnish with rosemary sprigs before serving, if desired.
Cut the pastry into squares and place a piece of backstrap on each one.