Prep your outdoor grill.
In a large frying pan add olive oil over medium high heat. Add the red onion slices and sauté for about 5-8 minutes or until soft and just starting to brown. Set aside in a small bowl.
In a food processor, add the sun-dried tomatoes, capers, cornichons, tarragon leaves, and parsley leaves. Pulse until mixture is chopped and combined.
In a large bowl, add the ground bison and sun-dried tomato mixture. Mix gently with your hands until combined. Shape into 4 burgers about 3/4 of an inch thick.
Grill burgers over medium high heat for about 5 minutes per side or until grilled to your preference. (Medium 140 degrees F internal temperature when measured with an instant thermometer.
Transfer the burgers to a platter and top with Parmesan cheese. Serve with whole grain French mustard and ketchup.