Preheat the oven to 350 degrees F.
Put the sweet potato in a medium saucepan with cold water to cover. Salt the water generously and bring to a boil.
Reduce the heat and simmer until the potato is just fork tender, about 6 minutes. Drain and cool. Peel the potato and dice it into 1/4-inch cubes.
Heat a medium skillet over medium-low heat. Add the duck breast skin side down and cook until the fat has rendered and the duck is warm, about 10 to 12 minutes. Remove from heat and place the duck on a plate.
Add 1 tsp. of olive oil to the pan. Add the smashed garlic cloves and rosemary and cook until fragrant, about 3 minutes.
Discard the rosemary and garlic.
Add the onion and cook until tender, about 4 minutes.
Add the celery and red pepper and cook until tender, about 3 minutes.
Season with 1 ½ teaspoons salt and some pepper. Add the minced garlic and cook about 2 minutes more.
Dice the duck meat into quarter inch pieces. Add the sweet potatoes, diced duck and chicken broth to the skillet and warm over medium heat, adding more stock if mixture seems dry.
Stir in the hoisin and hot sauce, and season, to taste. Remove from heat and stir in the chopped parsley and sherry vinegar.