Rinse carrot, tomatoes, cucumber, beets, and parsley. Remove the ends, peel, and shave carrot with vegetable peeler. Halve tomatoes. Peel, seed, and cut cucumbers into ¼” dice. Stem parsley. Peel red beet, cut in half, and slice into very thin, 1/8" half moon slices. Halve shallot, slice half into strips and mince other half. Mince garlic. Rinse edamame.