In the small pot, melt the butter on medium heat and add the garlic. Cook the garlic until aromatic but not brown. Don’t burn the garlic!
Add the sake to the pot to deglaze and cook the sake for 30 seconds.
Add in the chicken broth, yellow miso, both mustards, and sugar to the pot. Taste the broth to adjust salt. The salt level could depend on your taste and the particular chicken broth you have.
Bring all of the ingredients in the pot to a boil and turn down to a simmer. Simmer for 5 minutes, then turn off the pot.
Cut the hot dogs into 2” pieces. For fun, cut one end into quarters 1” from the top and leave the other end intact. Then cut those four strips in half to make eight strips, leaving it still attached on one end. When you cook these hot dog pieces it will appear like a baby octopus-shaped hot dog.
Shave the cabbage thinly with a knife.
Bring the seasoned broth back to a simmer and add in the cabbage. Cook gently for 5 minutes. Add in the hot dog pieces to warm through and allow the hot dogs to curl. Turn off the broth and keep it warm while you cook the noodles. Check the seasoning of the broth to make sure it did not become salty while cooking down. If it has become salty, add a small amount of water to adjust.
In another small pot, fill with hot water and bring to a boil. Once the water is boiling, add in the ramen noodles. Cook for 1–2 minutes, or according to the package instructions. Be careful not to overcook. Drain the noodles in a colander in the sink. Make sure they are drained well.
Add the hot noodles into four warmed bowls. Add in the hot broth on top of the noodles and four pieces of the hot dogs in each bowl. Garnish with thinly sliced scallions and serve.