Bring a large pot of salted water to a boil. Add the udon noodles and cook according to package instructions until tender, about 8-10 minutes. Drain and set aside.

In a skillet over medium heat, combine coconut milk, white miso paste, soy sauce, sesame oil, and rice vinegar. Whisk until smooth and heated through, about 5 minutes.

In the same skillet, add the sliced shiitake mushrooms and julienned carrot. Sauté for 3-4 minutes until softened. Add the spinach and cook until wilted.

Add the cooked udon noodles to the skillet with the creamy miso sauce and vegetables. Toss to combine and heat through for another 2 minutes. Serve hot, garnished with sliced scallions.