Make the Cowboy Butter by mixing softened butter with parsley, chives, garlic, Worcestershire sauce, lemon juice, smoked paprika, and cayenne pepper in a bowl.
Preheat the grill or grill pan over medium-high heat. Rub the flank steak with olive oil and season with salt and pepper. Grill for 4-5 minutes on each side for medium-rare, then let it rest for 5 minutes.
Slice the rested steak against the grain into thin strips. Spread Cowboy Butter on the bottom half of each slider bun, layer with steak slices, cheddar cheese, and arugula or spinach, then top with the other half of the bun.
Lightly toast the slider buns on the grill or in a toaster until golden brown before serving.