If using top round and brisket, in a large bowl, toss the meat, fat and spice mix together to combine. Attach the medium-sized die to a meat grinder and grind the beef and fat, then transfer to a medium bowl and mix gently until evenly combined. If using ground beef,form the meat into 4 patties, about 3/4-inch thick and, with the handle of a wooden spoon, make an indentation in the middle of each patty. (This will prevent the burgers from shrinking into meatball shapes while cooking). Season the patties on both sides, using 1 1/2 teaspoons salt and 1/2 teaspoon pepper for each one.
Heat 1 tablespoon of the olive oil in a large cast-iron skillet over high heat until smoking. Place the beef patties in the pan, immediately reduce the heat to medium-high, and cook for 4 minutes; do not press on the burgers so they retain their juices. With a spatula, carefully flip the patties; add the butter, garlic cloves and thyme to the pan. Once the butter has melted, tip the pan and baste each burger a few times, spooning the hot butter over it. Continue to cook, basting often, until the burgers are well-browned on the bottom and the meat is medium-rare, 5-6 minutes. Remove the burgers from the hot pan, top each with a slice of cheddar, and let rest for 5 minutes.
Meanwhile, prepare the bacon: Heat the remaining 2 teaspoons oil in another large skillet over medium-high heat. Cut the chilled bacon into 8 thin slices and cook on both sides until crisp, 3-4 minutes per side. Drain on paper towels.
To build the burgers, put 2 slices of tomato on each muffin bottom, followed by a burger. Top each burger with 2 to 3 tablespoons candied onions, some bacon and the top bun.
Serve immediately.