Gather all your ingredients so that you have everything close at hand on the counter or table. Using a sharp knife and cutting board, slice the onion.
Form the ground venison into 4-6 patties, depending on how big you want the burgers.
Heat a large cast iron skillet on medium-high heat and pour 1-2 tablespoons of olive oil on the skillet. This added oil is especially helpful when cooking venison, which tends to be very lean. If using ground beef, you may opt to omit the oil.
Cook the burgers 4-8 minutes on each side, until they've reached the preferred doneness that you desire.
If you'd prefer to grill the burgers, cook on a heated grill for 8-14 minutes, depending on the level of doneness you prefer.
To test for rareness, use a digital thermometer and the following guide to rareness: Rare burgers - 130°; Medium-rare burgers - 140°F; Medium burgers - 150°F; Well-done burgers, 165+ °F
When done, remove the skillet from heat and place cheese slices on the burgers. Allow to melt for a few minutes. Place burgers on a platter to keep warm until ready to serve. Cover with tented aluminum foil if more than 10 minutes.
Prepare the Fry Sauce
While the burgers are cooking, prepare the fry sauce. In a small bowl, combine ketchup, mayonnaise, Dijon mustard, red wine vinegar, and smoked paprika. Mix well to combine.
Cook the Onions
To cook the onions, place sliced onions on the same hot skillet that you cooked the burgers. Add some olive oil to the pan. Stir and saute on medium-low for 4-6 minutes, depending on how tender you like your onions.
Assemble the Burgers
When ready to serve, assemble the burgers on buns (grilled or not) with the sauted onions. Top with dill pickles, if desired. Generously spoon fry sauce over burgers and use any extra sauce for French Fries. Makes 4-6 burgers.
Notes
*Unless otherwise indicated all butter used on this recipe site is salted.