Heat olive oil in a skillet. Add mushrooms and saut? until golden. Stir in soy sauce, mirin, and brown sugar. Cook until mushrooms are caramelized and glossy. Set aside.

In a large pot, heat sesame oil. Add garlic and ginger, saut?ing until fragrant. Pour in vegetable broth and bring to a gentle simmer.

In a small bowl, whisk miso paste with a ladle of warm broth until smooth. Stir back into the pot to avoid clumps. Add soy sauce and stir well.

Add udon noodles directly into the broth if fresh, or cook separately if dried. Simmer until warmed through and tender.

Divide noodles and broth into bowls. Top with teriyaki mushrooms, green onions, and strips of nori if using. Serve steaming hot.