Arrange all the hot-pot ingredients on their own plates and in their own ramekins. Set the plates and ramekins on the table with a portable gas burner.
In a Dutch oven or hot-pot dish, bring the dashi, sake, soy sauce, mirin, garlic and pepper flakes to a simmer. Season the broth to taste with kosher salt.
Transfer the Dutch oven or hot-pot dish to the portable burner (at the table). Return the broth to a simmer.
Cook all the ingredients, except the udon, in the order listed (longest cooking time to shortest cooking time). Keep the broth simmering at all times. Add more stock as needed.
Transfer cooked food to the serving plates, adding fresh broth as needed. Strain the broth and return it to a simmer. Add the udon noodles and cook until tender, 10 to 12 minutes.