Check items off while grocery shopping - it’s remembered here.
Boil 4 cups water with a large sheet of kelp; once it comes to a boil, remove the kelp and strain.
Blend 2 tomatoes and 1 clove garlic in a mixing bowl, then add 1.5 cups of the kelp stock, 2T soy sauce, 1T mirin, 1t lemon juice, 0.5T plum extract, and a pinch of salt and pepper, and mix well. (Chill in the fridge, or serve over ice for a cold dish.)
Boil the buckwheat noodles, adding a splash of cold water to the pot about three times as it boils.
Place the noodles in a bowl, pour over the broth from step 2, and top with tomato and pickled melon. Finish with a little black sesame and sesame oil.