Pour sesame oil into a pan and place over medium heat. Add shallots and bok choy 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, ginger, garlic, green onion and cooled bok choy mixture. Season mixture well with salt and pepper and mix together until everything I 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 potsticker in half, making sure to get rid of any air pockets before completely sealing. You should be left with a half circle. Transfer to a clean plate, resting sealed side up.
Repeat steps 4 and 5 until all filling and wrappers have been used.
Pour 1 tablespoon oil into a large 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.
Pour ¼ cup water into the side of the skillet and quickly cover the skillet with a lid for about 3 to 4 minutes or until steam dissipates and potstickers have cooked though completely.
Repeat steps 7 through 9 until all potstickers have been cooked through. Serve with a side of soy sauce for dipping.