MAKE THE GLAZE: Combine the root beer, brown sugar, ketchup, lemon zest, and mustard in a small saucepan and bring to a simmer over low heat. Cook, stirring often, for about 10 minutes, or until the mixture is saucy and coats the back of a spoon.
HEAT A LARGE SAUTÉ PAN (or grill pan) over high heat until very hot. Pat the duck breasts dry with a paper towel and lay them skin-side down in the pan. Reduce the heat slightly, to medium-high, and cook undisturbed for 5 minutes.
TOAST THE SESAME SEEDS: Place the seeds in a small pan over medium heat. Shaking the pan occasionally, cook until the seeds turn golden and fragrant, about 3 minutes, being careful not to scorch them. Remove from heat and let cool.
FLIP THE MEAT OVER and generously brush with the root-beer glaze. Cook for 2 minutes, or until just medium-rare. Flip again, brush the meat side with the glaze, and remove to a cutting board. Cover with foil and allow to rest about 5 to 8 minutes.
REMOVE THE DUCK BREASTS from the refrigerator about 15 minutes before cooking, and salt. (If using domestic, farm-raised ducks, score the skin with a sharp knife, in a crosshatch pattern.)
TO SERVE, SPOON ANY REMAINING GLAZE onto the breasts and sprinkle with the toasted sesame seeds, then slice. Mashed sweet potatoes make a fine accompaniment.