Form the Patties - Without mixing the ground beef, portion it into 4 even-sized mounds, 6 ounces (about ⅓ pound) per patty. Gently form each portion into a loose ball. Press each one down to a ¾-inch thickness by about 4 ½-inches wide. Reshape the sides into a circle. It’s okay if the edges are jagged.Create an indent in the center of each patty, about ½-inch deep. If the patties feel warm after handling, chill them before grilling so they hold their shape better. Refrigerate if not using within 10 minutes of shaping.
Season the Surface - Right before grilling, generously season each side with salt, pepper, garlic powder, and onion powder.
Make the Burger Sauce - In a small bowl, combine mayonnaise, ketchup, relish, honey, vinegar, and black pepper.
Set up the Grill - Using a two-zone fire configuration (one side direct heat, the other side indirect heat), cover, and preheat for 5 to 10 minutes until the grates are hot. Clean the grates, and grease with oil to prevent the burgers from sticking.
Grill the Burgers - Place each burger on the direct heat side of the grill. Do not press down on the patties. Cook until deep golden brown on the first side, 3 to 5 minutes. Flip and cook until the desired doneness (see notes) is reached, about 2 to 5 minutes. If a medium-well or well-done burger is desired, transfer to the indirect side after flipping and cook for 2 minutes to gently complete the cooking process.
Melt the Cheese - If using cheese, add to the patties about 1 minute before reaching the desired doneness. Move the patties over to the indirect heat side, add the cheese on top, cover, and allow it to melt.
Toast the Buns - Transfer the burger patties to a plate, loosely cover with foil and rest for 5 to 10 minutes while heating the buns on the indirect heat side.
To Serve - Place patty inside toasted buns and add desired toppings and sauce.
Notes
Doneness: Stop cooking about 5 degrees before the desired doneness temperature. Medium-rare: 125-130ºF / 51-54ºC (pink with a hint of red in center). Medium: 135-140ºF / 57-60ºC (light pink center). Medium-well: 145-150ºF / 62-66ºC (brown with a hint of pink in center). Well-done: 150-160ºF / 66-71ºC (brown center).
Charcoal Grilling: Open the bottom vent of the grill. Light a chimney starter filled with charcoal briquettes, about 40 pieces for a smaller chimney. Use more if cooking 4+ burger patties. When the surface of the coals is partially covered with ash, pour them into the grill on one side to create a two-zone fire. Let them sit in a pile until most turn gray, about 5 minutes. Then evenly spread the coals out, but still keeping two zones. Place the cooking grate over the hot coals, cover, and open the lid vent.
Gas Grilling: Turn burners to high, leaving one area for indirect heating. Cover and allow the grill to heat up to about 400 to 450ºF (204 to 232ºC).