Preheat oven to 375˚ F.
Pat duck breasts dry with paper towel. Rub lightly with olive oil, salt and pepper.
Heat cast iron skillet over high heat. When pan is very hot, put duck breasts in, fat side down. Let duck sizzle for 60-90 seconds. Immediately transfer pan from stovetop to oven.
After 2 minutes, use tongs to flip breasts over in pan and continue to cook for another 2½ minutes. Remove pan from oven, transfer duck to platter and let rest for 5 minutes. (Test for doneness: internal temperature of 130˚F for medium-rare.)
While duck is resting, prepare sauce. In a small saucepan, combine remaining ingredients. Cook on medium heat, stirring occasionally, until thick and syrupy in consistency, 4-5 minutes.
Slice duck breasts and serve with generous drizzle of sauce.