Preheat your oven to 400°F and line a baking sheet with parchment paper.
Slice the wonton wrappers into thin strips, toss them in a bowl with avocado oil and sea salt, then spread them on the baking sheet and bake for 5-7 minutes until golden and crispy.
In a large pot, combine the chicken bone broth, minced ginger, minced garlic, and sliced shiitake mushrooms.
Bring the mixture to a gentle simmer over medium heat and stir in the tamari and white pepper, allowing the flavors to meld for 5 minutes.
In a small ramekin, whisk the arrowroot powder with the cold water to create a smooth slurry.
Stir the arrowroot slurry into the simmering broth and continue to cook until the liquid thickens slightly.
In a separate bowl, lightly whisk the whole eggs and liquid egg whites together until just combined.
Using a spoon, stir the soup in a circular motion to create a slow whirlpool, then slowly drizzle the egg mixture into the broth to form delicate ribbons.
Add the frozen peas to the pot and cook for 1 minute until they are bright green and heated through.
Turn off the heat and stir in the toasted sesame oil and sliced green onions.
Ladle the soup into a large bowl and top with the crispy wonton strips just before serving.