If using eggs, place the eggs in a small pot and cover with water by 1 inch. Over high heat, bring to a rolling boil. As soon as the water boils, remove from heat. Cover and let stand for 14 minutes. Drain and rinse with cold water, and place in an ice water bath to speed cooling. Peel the eggs and reserve.
In a medium pot, warm the avocado oil over medium heat, add the ginger, and stir for about a minute to soften.
Add the water, tamari, rice vinegar and pepper flakes and bring to a boil.
Add the mushrooms and return to a boil for a few seconds, then add peas and simmer briefly until crisp-tender.
Ladle half a cup of the hot soup into a small bowl and use a fork to stir the miso into the broth until smooth. Return the miso broth to the pot.
Place halved eggs in two wide bowls, ladle 2 cups of soup over each, and serve.
