Put a rack in middle of oven and preheat oven to 450 degrees F. Line a baking sheet with parchment.
Whisk together mustard, vinegar, salt, and 1/4 teaspoon pepper in a large bowl. Add chicken, tossing to coat well.
Pulse English muffins in a food processor until finely ground. Add cheese, butter and remaining 1/4 teaspoon pepper and pulse until well combined. Transfer to a shallow dish or pie plate.
Dredge chicken one piece at a time in crumbs, coating completely and pressing gently so crumbs adhere then transfer to baking sheet. Bake until golden brown, and cooked through, 15 to 20 minutes.