Spread the baguette pieces on a baking sheet. Brush with olive oil and season with salt and pepper. Bake 8 to 10 minutes, until crisp and light golden brown. Set aside.
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 legs skin side down and cook until the fat has rendered and the duck is warm, about 10 to 12 minutes. Remove the duck to a plate. If the skillet seems dry, add a bit of olive oil. 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 the 1 1/2 teaspoons salt and some pepper. Add the minced garlic and cook about 2 minutes more.
While the vegetables cook, remove the skin from the duck legs and discard. Shred the duck meat into long strips. Add the sweet potatoes, shredded 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. To serve, top each baguette slice with 1 heaping tablespoon of the duck hash.
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