Heat water in a large pot over low heat. Add kombu and cook until just simmering. Stir in bonito flakes, then remove dashi stock from the heat. Let dashi sit, uncovered, for 5 minutes. Strain and set aside.

Heat 3 1/2 cups dashi in a pot over medium heat. Add tofu and wakame and stir to combine. Remove 1 cup warmed dashi to a small bowl and whisk in miso paste. Pour miso mixture back into the pot with remaining dashi. Stir until warmed through. Serve garnished with chopped green onions.