In a skillet over medium heat, melt the butter and add the olive oil and sliced onions. Sprinkle with a pinch of salt. Cook the onions, stirring occasionally, for about 15-20 minutes, or until they are soft and golden brown. Remove from heat and set aside.

In a large bowl, combine the ground turkey, Parmesan cheese, garlic, lemon zest, salt and pepper. Mix until just combined. Form the mixture into small patties, about the size of your slider buns.

Heat olive oil in a skillet over medium-high heat. Add the turkey patties and cook for about 4-5 minutes on each side, or until they are cooked through and reach an internal temperature of 165°F
(74°C). During the last minute of cooking, place 2 small pieces of cheese on each patty and cover the skillet to melt the cheese.

Toast the slider buns if desired. Dress the bottom but with mayonnaise. Place each turkey patty on a bun, top with caramelized onions, and drizzle with banana pepper sauce.