Lay duck out on flat surface and cut slits in skin. Sprinkle on both sides with paprika and salt and let sit uncovered in cooler for 8 hours. Place duck skin side down in a hot saute pan over medium heat. Cook until fat has been rendered and skin begins to brown. Turn over to sear other side and place in a preheated 400 degree oven on a rack skin side up. Cook until medium rare about 8 minutes. Remove duck from oven and let rest. While duck is resting, pour off half the fat in pan. Add zest, juice and vinegar and whisk. Cut endive into quarters through the length of the head, and add to pan. Simmer for about 2 minutes until endive gets tender. Remove pan from heat and add mint and orange segments. Check seasoning. Slice each duck breast into 4 pieces and place over endive. Spoon 2 tablespoons of sauce over duck and serve.
Recipe courtesy of Michael Symon