In a large Dutch oven or high-sided pot, heat the sesame oil (and olive oil if needed) over medium-high heat. Add the shiitake mushrooms, shredded carrots, about two-thirds of the sliced green onions (reserving the rest for garnish), minced garlic, and grated ginger. Sauté for about 4 minutes, stirring frequently, until the mushrooms and carrots begin to soften.

Pour in the chicken broth. Add the soy sauce, honey, salt, and black pepper. Bring the mixture to a boil.

Once boiling, add the bok choy. Let it simmer in the broth for about 3-5 minutes, or until wilted.

Add the frozen wontons to the pot. Simmer for about 3 minutes, or until they are cooked through. They typically float when done. You don't need to fully thaw them before adding; they will cook in the broth.

Taste the soup and adjust seasonings as needed. Add more salt, pepper, or a pinch of red pepper flakes for extra spice if desired.

Ladle the soup into bowls. Garnish with the remaining sliced green onions and optional fresh cilantro or herbs. Serve immediately.