Preheat a grill pan over medium-high heat. In a large bowl, combine the beef, allspice, cayenne, pepper flakes, garlic powder, onion powder, oregano, brown sugar, thyme, salt adn black pepper and gently mix until combined.
Form the meat into eight 2-ounce patties, then press te center of each wit your thumb to create an indent. Coat the grill pan with cooking spray.
Grill the sliders indent side up until the internal temperature reads 150 degrees, 2-3 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 a cover loosely with foil to rest.
While the patties rest, brush the buns with melted butter and grill until lightly toasted, about 2 minutes per side.
Assemble the sliders by putting a tablespoon-sized dollop the ketchup on the top and bottom of the bun with the patty, finishing with one onion ring on top of each slider.
In a nonreactive medium bowl, combine the ketchup, lime juice, brown sugar, cayenne, pepper flakes, and salt and mix until incorporated. Use immediately or transfer the ketchup to an airtight container and refrigerate for up to 4 days.