In a mixing bowl, combine the white miso paste, soy sauce, sesame oil, rice vinegar, sugar, minced garlic, and grated ginger. Mix well until smooth.

Set the marinade aside to allow the flavors to meld.

In a large bowl, add the sliced shiitake and button mushrooms.

Pour the miso marinade over the mushrooms and toss until they are evenly coated.

Let the mushrooms marinate for at least 15 minutes.

Heat a skillet over medium heat and add the marinated mushrooms along with the marinade.

Cook for about 10-15 minutes, stirring occasionally, until the mushrooms are tender and the marinade has thickened.

Remove from heat and transfer the mushrooms to a serving dish.

Garnish with sliced green onions and toasted sesame seeds before serving.