Cook the udon noodles according to the package instructions. Drain and set aside.
In a large pot, bring the vegetable broth to a simmer.
In a small bowl, whisk together the miso paste and some of the hot broth until smooth. Stir the miso mixture into the pot of broth.
Add the tofu, green onions, shiitake mushrooms, spinach leaves, soy sauce, mirin, and sesame oil to the pot. Simmer for 10-15 minutes, until the vegetables are tender and the flavors have melded together.
Divide the cooked udon noodles among bowls and ladle the hot miso broth over the noodles.
Serve hot and enjoy!