Preheat the oven to 375°F.
Heat a large skillet over medium heat and add olive oil and diced potatoes. Cook for about 5 minutes, stirring occasionally.
Add onions, shallots, and garlic, and cook for an additional 5 minutes.
Add ground elk and cook until browned. Season with dried tarragon, parsley, and salt. Remove from heat and transfer the mixture to a bowl.
Spoon the elk and potato mixture into a pie plate, then top with the cooked mushrooms and shredded cheese.
Carefully place the pie crust over the filling and crimp the edges. Cut slits in the crust to allow steam to escape.
Bake 30–40 minutes, covering the crust edges with foil during the last 15 minutes to prevent over-browning.
Let stand 5 minutes before serving.