Bring a medium pot of water to a boil. Add ramen and cook, breaking up noodles as they soften, until tender yet firm to the bite, about 3 minutes. Drain, rinse with cold water, and drain again. Divide noodles between two soup bowls.
While the ramen is cooking, bring 2 1/2 cups water to a boil in a separate pot. Stir in soy sauce, mirin, dashi powder, and rice vinegar. Reduce the heat to low and add mushrooms, green onions, and ginger; simmer until mushrooms are tender, 3 to 5 minutes. Turn off the heat and cover to keep warm.
Melt butter in a skillet over medium-high heat. Add scallops and cook until opaque in the middle and golden brown on the edges, about 2 minutes per side.
Pour 1/2 of the hot stock into each bowl over ramen, then top with scallops.