Heat oven to 400° F. In a food processor, pulse the bread, parsley, garlic, and ¼ teaspoon each salt and pepper until coarse crumbs form.
Add the oil and pulse to combine. Transfer to a plate.
Spread the mustard over the chicken and dip the pieces in the bread-crumb mixture, pressing gently to help it adhere.
Place the chicken on a baking sheet and bake until golden and cooked through, 18 to 20 minutes. Serve with parsley sprigs (if desired).