Prepare the mulled wine a day ahead. Add all the ingredients to a pot, bring to a boil, turn off the heat, let the mulled wine steep, and let cool. Marinate the duck in the mulled wine and refrigerate overnight.
The next day, remove the duck from the fridge and generously season with salt and pepper. Preheat the oven to 325°F and pour the mulled wine into a carafe. Place the carafe on a baking tray and place the duck upright on the carafe.
Peel the potatoes and carrots and cut them into ¾-inch thick pieces. Use festive cookie cutters to cut out themed pieces. Spread the vegetables around the carafe on the baking tray and drizzle olive oil over them. Add rosemary sprigs, season with salt and pepper, transfer the baking tray to the oven, and cook for 2 hours.
For the mulled wine gravy, caramelize the powdered sugar in a pot, add the dried cranberries, and deglaze with mulled wine from the carafe. Add the red wine vinegar, let the sauce reduce down a bit before, add the chicken broth, season with salt and pepper, and let everything boil down.