In a medium bowl, combine the ground chicken with grated ginger, minced garlic, half of the sliced green onions, sea salt, and black pepper.
Place one teaspoon of the chicken mixture in the center of each wonton wrapper, moisten the edges with water, and fold into triangles, pressing firmly to seal.
Heat the avocado oil in a large non-stick skillet over medium heat and arrange the wontons in a single layer.
Sear the wontons for 2 to 3 minutes until the bottoms are golden brown and crispy.
Carefully pour two tablespoons of water into the skillet and immediately cover with a lid to steam for 4 minutes.
While the wontons steam, cook the shelled edamame in a small pot of boiling water for 3 to 5 minutes until tender.
In a small bowl, whisk together the tamari, toasted sesame oil, rice vinegar, and the remaining green onions to create the dipping sauce.
Remove the lid from the skillet and allow any remaining water to evaporate before plating the wontons.
Serve the crispy wontons immediately alongside the steamed edamame with the dipping sauce on the side.