Preheat oven to 450°F and line a baking sheet with parchment.

Whisk together mustard, vinegar, salt, and 1/4 teaspoon pepper in a large bowl and add chicken breasts, 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 combined well. Transfer to a shallow soup plate or pie plate.

Dredge chicken, 1 piece at a time, in crumbs, coating completely and pressing gently to help crumbs adhere, then transfer to baking sheet. Bake in middle of oven until golden brown and cooked through, 15 to 20 minutes.