For the cranberry compote: Whisk together the sugar, rice vinegar and rum in a bowl, then pour into a saucepan. Add the cranberries and bring to a simmer over medium heat. Cook until reduced and syrupy and the cranberries are plump, 10 minutes. Cool to room temperature.
For the cauliflower puree: Bring the cream to a boil in a medium saucepan. Add the cauliflower and bring to a medium simmer. Cook until the cream is reduced by a third and the cauliflower is fork tender, 7 to 10 minutes.
Transfer the cauliflower and half of the reduced cream to a food processor and process until smooth. Add salt and pepper to taste. If you want a thinner puree, add more cream.
For the fried Brussels sprouts: Heat the vegetable oil in a deep fryer. Add the Brussels sprouts and fry until light golden brown, 1 to 2 minutes. Drain well and toss with salt and pepper to taste.
For the duck breasts: Prepare a grill for medium-high heat. Whisk together the five-spice powder, cayenne, garlic powder, onion powder, paprika, brown sugar, thyme and 2 tablespoons each salt and pepper.
Liberally coat the duck breasts on both sides with the spice mixture. Grill skin-side down until crispy and the fat is rendered, 3 to 5 minutes. Flip the breasts and continue cooking to an internal temperature of 140 to 150 degrees F, about another 3 minutes. Let rest for 5 to 7 minutes before slicing into 1/2-inch medallions.
To serve: Arrange some slices of duck breast atop a smear of cauliflower puree. Top with compote and scatter fried Brussels sprouts around the plate.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.