Preheat a grill pan over medium-high heat. In a large bowl, combine the beef, allspice, cayenne, red pepper flakes, garlic powder, onion powder, oregano, brown sugar, thyme, salt and black pepper and gently mix just until combined.
Form the meat into eight 2-ounce patties, then press the center of each with your thumb to create an indent. Coat the grill pan with cooking spray.
Grill the sliders until the internal temperature reads 150˚, 2 to 3 minutes per side. Place a slice of cheese on each patty once you flip them. The cheese will melt over the sides of the patties. Remove the patties to a plate and cover loosely with foil to rest.
While the patties rest, brush the buns with the melted butter and grill until lightly toasted, about 2 minutes.
Assemble the sliders by putting a tablespoon-size dollop of the ketchup on the top and bottom buns, topping the bottom bun with the patty and finishing with an onion ring on top of each. Serve with the remaining onion rings and ketchup on the side.