Whisk the Dijon mustard, honey, mayonnaise, apple cider vinegar, and salt until smooth. Refrigerate while preparing the sliders.
Pat the chicken dry. Toss with the oil, smoked paprika, garlic powder, onion powder, oregano, salt, black pepper, and optional cayenne.
Heat a large skillet or grill over medium-high heat. Cook the chicken for 3 to 4 minutes per side until browned and the thickest pieces reach 165°F (74°C). Rest for 5 minutes.
Heat the broiler. Split the rolls and arrange both halves cut-side up on a rimmed baking sheet. Broil for 1 to 2 minutes until lightly golden.
Spread honey mustard over each bottom roll. Add chicken and cheese, then broil for about 1 minute until the cheese melts.
Layer on the bacon, tomato, red onion, and lettuce. Drizzle with more honey mustard.
Mix the melted butter, garlic, and parsley. Brush over the roll tops, place them on the sliders, separate with a serrated knife, and serve immediately.