For all the mushroom, rinse and pat dry with paper towels. For the shiitake, cut off the stems and cut into stripes. For the oyster, remove stem and cut into 1-inch long stripes. For the white beech, brown beech, and makitake, trim the base of the cluster. Pull the mushrooms apart. For enoki, trim the base of the cluster and pull the mushrooms apart into small bunches.
Bring a large pot of water to a boil. Follow the udon package direction to cook the udon. Save 1 cup of udon water. Drain and rinse under cold water. Set aside.
In a large skillet over medium high heat, warm 1 tablespoon vegetable oil. Add half of the mushrooms and cook until nicely browned, about 4 – 5 minutes. Transfer to a medium bowl. In the same skillet, add another tablespoon oil. Cook the rest of the mushrooms until nicely browned. Transfer to the bowl with the other mushrooms.
In a small bowl, whisk together miso and 1/3 cup udon water until smooth.
In the same skillet over medium heat, melt the butter. Add garlic and cook for 1 minute. Add mushrooms, miso water, heavy cream, soy sauce and black pepper. Mix well. Add the udon and coat with the sauce. Cook for 2 more minutes. Taste and adjust the seasoning. Add more miso and soy sauce if needed. If the sauce is too thick, add a bit more udon water. Transfer to serving plates. Top with green onion and nori.