Heat avocado oil in a large pot over medium heat. Add the onions and cook, stirring regularly, for 5 minutes until they just begin to soften.
Cook the shiitake mushrooms: Add the sliced shiitake mushrooms to the onions and cook for 5 to 6 minutes. Season with salt and pepper.
Simmer the broth:
Add the mirin and soy sauce to the mushrooms. Pour in the vegetable stock and bring to a boil. Reduce heat and simmer for 30 minutes.
Prepare the radishes:
Cut the radish greens from the radishes. Rinse the radish greens thoroughly and set aside. Scrub the radishes and thinly slice them into rounds.
Toss the sliced radishes with sesame oil, shichimi-togarashi, salt, and sesame seeds and set aside.
Prepare the miso:
Combine the miso paste, tahini, and chili oil in a bowl and whisk until mostly smooth. Set aside.
Cook the noodles:
Right before the broth finishes simmering, add the noodles to a large pot of boiling water. Drain and divide the cooked noodles between four bowls.
Finish the ramen broth:
Turn the heat down to very low on the broth. Whisk in the miso mixture. Add the green beans and radish greens and allow the heat from the broth to cook the beans. Once the beans are bright green and tender-crisp, turn off the heat. Taste and season to your preferences.
To serve:
Ladle the hot broth over the ramen noodles. Arrange the sliced, dressed radishes on top. Enjoy!