Roughly chop the duck mixture along with some of the braising liquid.

In a small bowl, whisk the egg with a little water. Lay out the gyoza wrappers, four at a time. Keep remaining wrappers covered so they do not dry out.

Spoon 1 1/2 tablespoon of the chpped duck misture onto the center of the wrapper. Using a pastry brush or your finger, brush a little egg wash around the edges of the wrappers. Place a second wrapperover the filling and press to smooth and release any air bubbles. Press all around the edges using the tines of a fork to fully seal. Continue this process until you have used all of the braised duck mixture. Place the ravioli on a baking sheet lined with parchment paper and dusted with flour. Keep covered with a damp paper towel until you are ready to cook.

In a small saucepan, bring the apple cider to a boil and continue to cook until reduced to 1/4 cup, about 13 to 15 minutes. Add the braising liquid and chicken stock, return the sauce to a boil and continue to cook for 3 minutes longer. Strain the sauce through a fine mesh sieve and return it to the saucepan. Bring to a simmer and slowly whisk in the butter a little at a time. Season with salt and pepper and set aside.

Meanwhile, bring a large pot of water to a boil and season with salt. Add the ravioli, three or four at a time, to the boiling water and cook for 3 to 5 minutes. Remove from the pot to a baking sheet rubbed with olive oil.

To serve the ravioli, place four ravioli in a large shallow bowl, ladle 1 to 2 ounces sauce over the ravioli and garnish with the brunoise apple and chiffonade of kale.