Heat water in a large pot over low heat. Add kombu and cook until the mixture just begins to simmer. Stir bonito flakes into kombu mixture until combined. Remove pot from the heat and let dashi sit, uncovered, for 5 minutes. Strain through a fine sieve and set aside.
Heat 3 1/2 cups dashi in a pot over medium heat. Add tofu and wakame; 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.