In a large mixing bowl, combine the ground beef, egg, cumin, mustard, garlic, oregano, soy sauce, teriyaki sauce, savory, dill, and black pepper. Mix with your hands until the seasoning is evenly distributed — about 1 minute. If using extra-lean ground beef, add 2 tablespoons of fresh breadcrumbs to the mixture. Alternatively, place all ingredients in a large resealable bag and knead through the plastic.

Place the beef mixture on a sheet of parchment paper. Press or roll it into a rectangle approximately 9×13 inches (23×33cm), slightly larger than the footprint of your roll pack. The patties will be thin — roughly ¼ inch (6mm) thick. The mixture will feel softer than typical burger meat because of the egg binder, but the patties will hold together on the grill.

Using a sharp knife or bench scraper, cut the rectangle into 12 equal pieces (3 rows by 4 columns). Preheat your grill to medium-high heat (around 400°F / 200°C). Grill the sliders for 3 minutes per side without moving them until it is time to flip. The internal temperature should reach 160°F / 71°C for ground beef. Serve on Hawaiian sweet rolls — these sliders are flavorful enough to eat plain, but grilled onions or a slice of cheese are excellent additions.