Defrost the refrigerated pie crust and preheat the oven to 375°F.
Heat a skillet over low heat. Add 2 tablespoons butter, olive oil, mushrooms, onions, and rosemary. Cook until the onions are caramelized, then remove from heat.
In a bowl, season the ground elk with granulated garlic, salt, and pepper. Form 4 equal-sized patties and set aside.
On a clean surface, roll out the pie crust and divide it into 4 equal sections. In the center of each section, layer a slice of Swiss cheese, the mushroom-onion mixture, and an elk patty.
Pull the corners of the pie crust up around the burger and flip so the seam is on the bottom. Place on a parchment-lined baking sheet.
Melt remaining butter and brush the tops of the wrapped burgers. Sprinkle with sesame seeds.
Bake for 45 minutes, or until golden brown. Let cool slightly before serving.