Place the chicken pieces in a stockpot or large Dutch oven with the unpeeled onion, 2 unpeeled garlic cloves, 1 teaspoon salt, black peppercorns, and mint; add water to cover by 2 inches (about 7-8 cups). Bring to a boil over high heat. At once, reduce the heat to maintain a low, rolling boil; skim off any foam that rises to the top. Cook, partly covered, until the chicken is tender, about 20-25 minutes. Remove the pot from the heat and let the chicken cool in the stock; lift out the chicken pieces, discard the skin and bones, and pull the chicken meat into shreds. Strain the stock, discarding the solids and reserve for another use.