For the duck:

Score the fatty side of the duck breasts in a crosshatch pattern, season the fat side with salt and pepper, to taste, and place in a large saute pan over high heat. Allow the fat to render until the side in the pan is a deep brown, about 6 minutes. Turn the duck breast over, season meat side with salt and pepper, to taste, and continue cooking, another 4 to 5 minutes. Remove the duck to a plate and cover loosely with foil. Pour off all but 2 tablespoons of the duck fat, and in the same saute pan over high heat, add the butter and persimmons. Allow the persimmons to soften slightly and add the shallots and sugar. Using a wooden spoon, stir the mixture until it incorporates. Turn the heat to medium-low and add the orange juice. When the mixture has reduced by 1/2, slide the duck breasts into the pan along with any accumulated juices and coat the duck with the glaze. Remove the pan from the heat and serve duck with cauliflower.

For the cauliflower:

Set a stock pot on the stove with a steamer insert and about a quart of water and the star anise. Cover and turn to high. When the water reaches a boil, add the cauliflower and let cook until just softened, about 4 minutes. Remove to a large bowl and toss with sesame oil, sesame seeds and ponzu. Season with salt and pepper and serve.