In a large bowl, combine all Elk Patties ingredients and gently mix until just combined. Form into 6 patties.
Heat Olive Oil in a skillet over medium heat. Add Yellow Onions and cook, stirring occasionally, for 20-25 minutes, or until deeply caramelized. Stir in Balsamic Vinegar and Brown Sugar during the last 5 minutes.
Prepare the Horseradish Aioli by combining all Horseradish Aioli ingredients in a small bowl and mixing well.
Preheat grill to medium-high heat.
Grill the elk patties for 3-4 minutes per side, or until cooked through (160°F / 71°C). Top with Provolone Cheese during the last minute.
Lightly toast the Brioche Slider Buns.
Spread Horseradish Aioli on both halves of each bun. Place an elk patty on the bottom bun, top with Caramelized Onions, and cover with the top bun. Serve immediately.
