Bring a large pot of water to a boil. Cook udon according to package directions.
Make the miso sauce: In a small saucepan, combine the miso paste, sugar, and mirin. Bring to a gentle boil, lower the heat, and simmer for 2-3 minutes, whisking continuously. Set aside.
In a medium pot or saucepan, heat the butter until melted. Add the garlic, ginger, mushrooms, scallion whites, and a pinch of salt and sauté until the mushrooms are cooked down.
Add the tofu and cook another couple of minutes.
Add the cooked noodles (if you can time this well, add them right from the boiling water so the excess water will help to create the sauce).
Add the sweet miso sauce 2 tablespoons at a time and taste after each addition. You might not use all of it depending on your preference. If necessary, add water or broth to thin the sauce to your desired consistency.
Turn heat off and stir in half the scallion greens, nori, and sesame seeds. Taste and adjust seasonings, adding more sauce if necessary.
Portion into bowls and top with the remaining scallion greens, nori, and sesame seeds.