Step 1Make a brine for the chicken: In a large (roughly 8-quart) pot, heat the water, brown sugar and salt over medium-high heat until the sugar and salt are dissolved, about 3 minutes.
Step 2Remove from heat and stir in the bay leaves, white and black peppercorns, mustard seed and cloves. Stir in the ice to cool the brine.
Step 3Place the brine in a non-reactive bowl or container and add the chicken (make sure the chicken is submerged, weighting the chicken down if necessary). Cover and refrigerate for 24 hours.
Step 4Remove the chicken from the brine and drain. Set the chicken aside while you heat the oven. Heat the oven to 400 degrees. Place the chicken on a rack in a roasting pan.
Step 5Roast the chicken at 400 degree for 25 minutes, then reduce the heat to 350 degrees and continue roasting until a thermometer inserted into the thigh of the chicken reaches 165 degrees, 1 to 1 1/2 hours (timing will vary depending on the original temperature of the chicken and how quickly the oven temperature readjusts).
Step 6Remove the chicken and set aside until cool enough to handle. Discard the skin and remove the meat from the bones (the bones can be discarded). Dice the chicken into small pieces . You should have about 5 cups (about 2 pounds) of shredded meat. Cover and refrigerate the meat if not using immediately; the meat can be made up to 1 day before making the empanadas.
Step 1Heat the oven to 400 degrees. Rub the peppers with 2 teaspoons of the oil, and season each with a pinch of salt and pepper. Wrap the peppers in foil and roast in the oven until softened, about 30 minutes, checking every 10 minutes. Remove from the oven and set the foil-wrapped peppers aside until cool enough to handle. Peel and seed the peppers, and cut into a small dice.
Step 2Heat a large saute pan over medium-high heat. Add 2 teaspoons oil and saute the onions until translucent, stirring frequently, about 8 minutes. Remove from heat.
Step 3Assemble the filling: In a large bowl, combine the diced chicken, diced poblanos, onions, 1 1/2 teaspoons salt, 1 teaspoon pepper, cilantro, Thai sweet chile sauce and Oaxaca cheese. Taste and season with additional salt and pepper if desired. You should have a generous 6 cups of filling. Cover and refrigerate the filling until chilled, at least 1 hour, up to overnight.
Step 4Roll out the puff pastry 1 sheet at a time (refrigerate the other sheets until ready to use) on a lightly floured board. Cut out rounds using a 3 1/2-inch biscuit cutter. You should be able to cut 16 to 18 rounds from each pound of puff pastry.
Step 5Fill each round with about 1 1/2 tablespoons of the chilled filling. To fold the empanada, place the round in your hand. With the fingers of your other hand, press the filling down as you are clamping the pastry into a taco or moon shape. It may seem as if there is too much filling at first, but the dough will stretch as you press the filling down (this will give you a good ratio of filling to pastry). Seal the empanada by pressing the edges with your fingers; use a fork to crimp it and seal it completely. Refrigerate the empanadas until ready to fry.
Step 6To fry the empanadas, heat the oil in a large, heavy-bottomed pot until a thermometer inserted reaches 350 degrees. Fry the empanadas a few at a time until golden-brown, about 3 minutes. Drain on a rack or a paper-towel-lined baking sheet. Repeat until all the empanadas are fried. Serve immediately.