Burgers:

• 1 ½ pounds venison meat, cut into 1-inch chunks, partially frozen
• ¾ pound fatty pork butt, cut into 1-inch chunks, partially frozen
• 2 tablespoons unsalted butter
• 1 ½ cups diced onion
• 1 cup diced button mushrooms
• 1 pinch salt
• ½ cup plain Greek yogurt
• 1 tablespoon Worcestershire sauce
• 1 tablespoon coarsely ground black pepper

Sauce:

• ½ cup mayonnaise
• 2 tablespoons steak sauce
• 1 tablespoon Worcestershire sauce
• 1 ½ teaspoons lime juice

Sandwich Fixings:

• 6 teaspoons softened butter, or as needed
• 6 hamburger buns, split
• 1 pinch salt
• 12 slices pepper Jack cheese
• 6 (1/4 inch thick) slices tomato