Combine all jerk marinade ingredients in a small bowl.
Pour the marinade over chicken breasts in a shallow dish. Refrigerate for at least 1 hour or overnight.
Grill chicken over medium heat for about 8 minutes per side until fully cooked.
Let the grilled chicken rest for a few minutes, then slice it.
While the chicken grills, mix slider topping ingredients in a small bowl.
Spread melted butter on slider buns and toast them on a preheated grill for 1-2 minutes per side until golden.
Assemble sliders with Dijon mustard, Muenster cheese, jerk chicken, and the prepared topping.
Serve the sliders immediately to savor the flavors.