Heat oven to 400° F. In a food processor, pulse the bread, parsley, garlic, and 1/4 teaspoon each of 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 on a baking sheet and bake until golden and cooked through, 18 to 20 minutes.