For the dough: Whisk the flour with the salt and stir in the water until dough is shaggy. Turn onto a lightly floured board and knead briefly; dough should be soft and pliable but not too sticky. Rest, covered, while you make the filling and the sauce.
Place all the ingredients in a large bowl and mix until thoroughly combined. To check for seasoning, fry a bit in some hot oil until just cooked through. Adjust the seasoning as necessary.
For the sauce:
Combine all but the last 2 ingredients in a bowl for dipping. Sprinkle the basil and habanero over the top.
To Assemble and Cook:
Flour your work surface lightly and roll the dough, or pieces of it, about 1/8-inch thick (too thin and the dough will tear as you fill the dumplings). Cut out circles with a 3-inch round cutter. Cover the dough with a side towel or piece of plastic wrap as you work. Have a small bowl of water next to you. Place a scant tablespoon of filling in the middle of a dough circle, and press it so that it spreads slightly toward the side edges of the dough. Using your fingertip or a small pastry brush, wet the edge of the dough. Fold the dough up around the filling so that the filling sits on the work surface-that's the bottom of your dumpling-and the seam is between your fingers. Pleat the dough that is facing you, about 6 times, pressing it against the back to seal-only the front of the dumpling should be pleated. The corners of the dumpling should curl slightly away from you, toward the unpleated side. Heat a skillet, just large enough to accommodate the number of dumplings you want to cook over high heat. Add a thin coating of oil, heat, then add the dumplings in concentric circles. They should be touching. Cook until the bottoms are golden brown, 3 or 4 minutes (reduce the heat if they are browning too quickly). Add enough water to come about 1/4 of the way up the sides of the dumplings-it will spatter. Cover the skillet, adjust the heat so that the water is simmering, and cook for about 7 minutes. Uncover the skillet and, if there is water left, let it cook off. Check the dumpling bottoms-if they need to brown a bit more, let them, adding a bit more oil if necessary. Serve the dumplings immediately, drizzled with some dipping sauce and garnished with cilantro and lime wedges.
This recipe makes 48 dumplings-a large batch. If you halve the recipe, use the whole egg, and, if it's more convenient for you, just use 2 boneless duck breast halves. If you have the patience to shape all of the dumplings, just freeze some of them; they will keep, tightly covered, for 2 weeks.