If using konnyaku, put the torn pieces in a small pot of water, bring to a boil for 2 minutes, then drain. This gets rid of the faint mineral smell. Skip this step if you are not using it.
Heat the sesame oil in a large pot or Dutch oven over medium high heat. Add the pork in a single layer and let it sit for a minute before stirring. Cook for 3 to 4 minutes until no longer pink and lightly browned at the edges.
Add the daikon, carrot, sweet potato, konnyaku and shiitake. Stir for 2 minutes so the vegetables pick up the pork fat. Add the sake and let it bubble off for 30 seconds.
Pour in the dashi and bring to a boil. Skim off the grey foam that rises in the first couple of minutes, then lower the heat to a gentle simmer. Cover with the lid slightly ajar and cook for 15 to 18 minutes, until a knife slides into the daikon and sweet potato with no resistance.
Add the tofu and simmer for 3 minutes to heat through. Turn the heat down to the lowest setting.
Put the miso in a ladle or small bowl, add a ladleful of the hot broth and stir until smooth, then pour it back into the pot. Do not let the soup boil again after this. Taste, and add a little more miso if it needs salt.
Ladle into bowls and top with scallions and a pinch of shichimi togarashi. Serve with rice on the side.