Caramelize Onions: In a large cast iron pan over medium-low heat add butter and olive oil. When butter melts, add the onions and slowly stir. Continue stirring for 30 to 40 minutes or until the red onions have reduced and turned brown in color. Adjust heat as needed.
Pre-heat Grill: Prepare grill for direct grilling, with griddle over the direct heat, targeting 400 degrees Fahrenheit.
Prepare 1/4 pound balls of beef. Season one side with dry rub. Be sure to reserve half the rub for after they are on the grill.
Add olive oil to the griddle. After 1 minute place the seasoned side of the beef onto the griddle and smash the burger with a spatula. Then add the remaining seasoning to the top of the burgers. Close the grill.
After 6-8 minutes open the grill and check to see if browning occured. Once you see it, flip the burger, add the slice of cheese and cover the burgers with your covering tool. Close the grill lid and continue cooking for an additional 2 minutes.
After 2 minutes the burgers should be at least 160 degrees F with the cheese melted. Remove burgers from the grill.
Assemble Burgers: Add the burger to your bun and add your favorite toppings. We recommend lettuce, pickles, tomatoes, special sauce, and the caramelized onions from above.