In a large bowl, combine ground beef, onion, bell pepper, garlic, oregano, basil, salt, and pepper until just mixed. Form into patties slightly thicker than the buns.
In a small bowl, whisk together ketchup, mustard, mayonnaise, and pickle relish to create the secret sauce.
Heat a skillet over medium-high heat and cook the patties for about 3-4 minutes per side until browned. Top with cheese during the last minute of cooking to melt.
Toast slider buns in the skillet or oven until golden brown.
Assemble sliders by spreading sauce on the bottom bun and layering with a patty, chicken ham slice, and optional toppings.