Heat a dry sauté pan on medium heat, add in the anchovies and sauté for 2 minutes.
Place the sautéed anchovies, dashi konbu and water into a medium sized pot and quickly bring to a boil. Then, reduce heat and simmer for 5 minutes.
Strain the liquid through a strainer and into another medium sized pot. Place the pot of strained anchovy broth on medium heat and season with salt to taste, add in the shiitake mushrooms, mizuna and kamaboko and simmer for 2 minutes.
Add in the thinly sliced mochi and simmer for another minute, then serve hot.