Place the spaghetti, sesame dressing and 1 teaspoon toasted sesame seeds in a medium bowl and toss well with tongs to coat the spaghetti in the dressing. Transfer to a serving dish.
Fan the marinated tofu on the spaghetti and place the edamame and pickles on top of the noodles. Garnish with the remaining teaspoon sesame seeds and sprinkle with salt and pepper.
Place the hot water, rice vinegar, salt and sugar in a small mixing bowl and mix to dissolve the sugar and salt. Place the cucumbers in a 16-ounce airtight container and pour the vinegar mixture over them. Seal the container and refrigerate for 1 hour or overnight.