Prepare the burger sauce if using by mixing the mayonnaise, ketchup, mustard, vinegar, paprika, garlic powder, and relish in a small bowl. Set aside.
Divide the meat into four equal pieces. Use your hands to form them into roughly 6" discs.
Heat a large cast iron skillet, broiler, or grill on high heat.
Salt each patty generously and sprinkle pepper if desired. Place the patty on the hot surface and cook for 4 minutes. Flip, and continue to cook until cooked through, 3-4 minutes more. If desired, add a slice of cheese on top of each patty about 1 minute before it is finished, allowing it to melt.
Insert an instant-read thermometer into the center of the burger, it is done when the thermometer registers 160°F.
Remove the burgers and set aside on a platter. Reduce the heat and place each bun onto the hot surface and lightly toast, about 2 minutes.
Once toasted, compile the burgers with your desired toppings and sauces.