Step 1
Grind partially frozen venison meat and pork butt together using a meat grinder or food processor; transfer to a large bowl and cover with plastic wrap. Refrigerate for at least 1 hour.
Step 2
Heat unsalted butter in a skillet over medium-low heat; cook and stir onion mushrooms and 1 pinch salt in the melted butter until onion is soft and translucent 5 to 10 minutes. Remove from heat and cool.
Step 3
Gently mix ground venison-pork mixture onion mixture yogurt 1 tablespoon Worcestershire sauce and black pepper together in a bowl until just combined. Form into 6 patties and arrange on a large plate. Cover plate with plastic wrap and refrigerate for at least 1 hour.
Step 4
Mix mayonnaise steak sauce 1 tablespoon Worcestershire sauce and lime juice together in a bowl until smooth. Cover bowl with plastic wrap and refrigerate until serving time.
Step 5
Preheat oven to 225 degrees F (110 degrees C).
Step 6
Spread 1/2 teaspoon butter onto the inside of each split bun.
Step 7
Heat a non-stick pan over low heat; cook buns buttered sides down in the heated pan until lightly browned 3 to 5 minutes. Transfer buns to a baking sheet and keep warm in the preheated oven.
Step 8
Heat a non-stick skillet over medium heat; cook burgers sprinkling each side with a pinch of salt in the hot skillet until your desired degree of doneness is reached 3 to 4 minutes per side. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C).
Step 9
Top each burger with a tomato slice and two slices pepper Jack cheese. Remove skillet from heat and cover pan until cheese is slightly melted about 5 minutes. Spread 1 to 2 tablespoons of sauce onto the inside of each bun bottom. Add a cheese-tomato burger to each bun bottom; top each burger with bun top.