Mix all sauce ingredients together and adjust to taste. Set aside. Prepare a burger "station" or have all toppings on a cutting board ready for assembly.
In a 12-inch skillet, add duck fat or oil, then wipe around with a paper towel. Place the skillet over medium heat and allow it to preheat for about 4-5 minutes. Meanwhile, gently form each portion of ground beef into a ball, being careful not to overhandle the meat, just until it holds its shape without falling apart. Avoid excessive handling of the meat.
When the skillet begins to emit a slight smoke, indicating it's adequately heated, add two separate handfuls of sliced onions to the spots where each burger will be placed. Next, place a beef ball on top of each pile of onions. Using a firm stiff metal spatula, burger press, or the bottom of a can, press down on each one until they are roughly 4 to 4½ inches in diameter and about 1 cm thick. If needed, use a second spatula to apply downward pressure to ensure the burgers are smashed sufficiently.
Generously season burgers with steak seasoning of choice or salt and pepper.
Cook without moving until a golden-brown crust develops, about 2 minutes. Use the edge of the spatula to carefully scrape up and flip the patties one at a time, making sure to get all browned bits removed from the skillet. If using cheese, add now.
Continue to cook until patties are cooked to desired doneness - about 1 minute longer or when cheese has melted. Turn of heat. Remove skillet from the burner. Remove from pan and set aside on a plate.
Lightly butter the buns and toast each side on the skillet until they reach your desired level of doneness. You can toast both sides or just the insides according to your preference. Be mindful not to burn them; ensure the heat is off as needed.
Assemble the burgers or allow each individual to customize their own according to their preferences as they enjoy their meal.