Fill a large pot with lightly salted water and bring to a rolling boil. Drop in soba noodles and return to a boil. Cook uncovered, stirring occasionally, until tender yet firm to the bite, about 7 minutes. Drain.
Toss noodles with sesame oil in a medium bowl. Divide noodles evenly between the 5 containers.
Top noodles with edamame, carrot, green onions, and cilantro, dividing them evenly between the 5 containers. Place lids on containers. Pour 1/4 cup peanut sauce into each dressing container. Refrigerate until ready to eat. Mix 1 dressing container with 1 serving of soba salad to serve.