Pour sesame oil into a pan and place over medium heat. Add shallots and saute for 3 to 4 minutes. Lightly season with salt and pepper and remove from heat to cool.
In a large mixing bowl, combine ground chicken, green onion, ginger, garlic, and cooled shallots. Season mixture well with salt and pepper and mix together until everything is evenly combined.
In a small bowl combine egg and 1 tablespoon water. Whisk together.
Brush the edge of a wonton wrapper with egg wash and fill the center with 1 ½ tablespoons filling.
Fold potstickers in half, making sure to get rid of any air pockets before completely sealing. You should be left with a half circle. Wet the edge of the wontons with water and taking your finger, gently fold over the corner of the border into the dumpling. Continue to fold the border until the entire edge has been crimped. Repeat with remaining potstickers.
Transfer potstickers to a clean plate, resting crimp side up.
Repeat steps 4 and 5 until all filling and wrappers have been used.
Pour 2 ½ tablespoon oil into a medium skillet over medium-high heat and swirl skillet to cover entire bottom with oil.
Add about ⅓ of the potstickers to the skillet, seam side up and about ½ inch apart, and sear for 2 to 3 minutes. Flip and continue to sear for an additional 2 to 3 minutes.
Add 2 tablespoons water to the skillet and cover until water evaporates, to allow potstickers to cook through.
Remove from skillet and repeat steps 7 to 9 with remaining potstickers. Serve.