Bring 2 cups water to a boil in a saucepan. Cook ramen noodles in boiling water until tender, 2 to 3 minutes; drain. Rinse with cold water to stop cooking process. Divide noodles between 2 soup bowls.

Bring 2 1/2 cups water to a boil in a saucepan. Stir soy sauce, mirin, dashi no moto, and rice vinegar into the boiling water. Reduce heat to low. Add shiitake mushrooms, green onions, and ginger to the water; cook at a simmer until mushrooms are tender, 3 to 5 minutes. Pour about half the mixture over each portion of noodles.

Melt butter in a skillet over medium-high heat. Cook scallops in melted butter until opaque in the middle, about 3 minutes. Put 4 cooked scallops into each soup bowl to serve.