Heat 1 tablespoon neutral cooking oil in a large pot over medium heat. Add the shallot and cook for 3-5 minutes until it begins to brown and soften.
Add the garlic and cook for 1 minute until fragrant.
Add the dashi broth and bring to a low boil. Reduce heat and add the soy sauce, mirin, sesame oil, chili oil, and dry chives. Simmer for 30 minutes. Taste and season to your preferences.
Cook the Noodles:
Fill the medium pot with water and bring to a boil. Cook the noodles according to package instructions. Drain and drizzle with 1 teaspoon sesame oil and sprinkle with salt.
Broil the Vegetables:
Turn the broiler on. Arrange the sweet potatoes and cauliflower on a sheet pan and drizzle with the remaining 1 tablespoon neutral cooking oil. Season with salt and pepper. Transfer to the broiler and cook for 3-6 minutes or until the vegetables are charred and softened. Be careful not to burn them; check the vegetables every 2-3 minutes. Remove from the broiler.
Finish the Broth:
Add the vegetables to the simmering broth and cook for 2-3 minutes. Turn off the heat.
To Serve:
Divide the cooked noodles between bowls and ladle the broth and vegetables on top. Garnish with sesame seeds, chili oil, and shichimi-togarashi, if desired. Enjoy!