1. Preheat oven to 425°.
2. Remove and discard giblets and neck from capon. Trim excess fat. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Combine sugar, 2 teaspoons mustard, and 1/2 teaspoon salt; rub sugar mixture under loosened skin and over breast and drumsticks. Tie ends of legs together with twine. Lift wing tips up and over back; tuck under capon. Place capon, breast side up, on the rack of a broiler pan coated with cooking spray. Pour 1 cup water into bottom of pan; place rack in pan. Bake at 425° for 30 minutes.
3. Baste capon with 1 cup broth; loosely cover capon with foil. Reduce oven temperature to 350° (do not remove capon from oven). Bake at 350° for 30 minutes. Uncover and baste with remaining broth. Bake an additional 20 minutes or until a thermometer inserted in meaty part of thigh registers 165°. Remove from oven; let stand for 20 minutes. Discard the skin before serving.
4. Place a zip-top plastic bag inside a 2-cup glass measure. Pour drippings from pan into bag. Let stand 2 minutes (fat will rise to the top). Seal bag, and carefully snip off 1 bottom corner of bag. Drain drippings into measuring cup, stopping before fat layer reaches opening; discard fat. Pour drippings into a small saucepan; stir in shallots. Bring to a boil; reduce heat, and simmer for 2 minutes. Add remaining 1 1/2 teaspoons mustard and bourbon, stirring with a whisk; simmer 1 minute. Combine potato starch and 1 tablespoon water in a small bowl, stirring with a whisk; stir starch mixture into bourbon mixture. Simmer for 1 minute or until thickened. Remove from heat; stir in remaining 1/4 teaspoon salt, parsley, and pepper. Serve gravy with the capon.