In a large mixing bowl, sprinkle the edamame pods with salt and let stand for 15 minutes. Bring a large pot filled with water to a boil over high flame. Boil the edamame for 6 minutes. Remove to a bowl and wash with cold water until cool to the touch. Set aside.
Meanwhile, in a small mixing bowl, whisk together the vinegar and sugar with a pinch of salt. Add the turnip and stir to combine. Set aside. With the heel of a knife, gently smash the cucumbers. Place into a mixing bowl with the lemon juice and a pinch of salt. Stir to combine and set aside.
In a saucepan over a medium flame, heat 1 Tbsp. oil until hot. Add the ginger and stir until fragrant, about 1 minute. Add the scallions and reduce the flame to low. Season with a pinch of salt and continue to stir until soft and the scallions begin to "melt,” about 15 minutes.
In a large sauce pan over high flame, heat the remaining oil until hot. Add the squash and stir, cooking until slightly soft, about 4 minutes. Add the tofu and continue cooking until browned on all sides, about 10 minutes.
Strain the turnips and divide evenly among 4 plates along with the mizuna, edamame and smashed cucumbers. Top with the tofu, squash and ginger scallion sauce. Season with the dulse flakes and salt to taste.