Use a vegetable peeler to shave the carrots into thin wide ribbons; discard the last thick strip. Transfer the carrot ribbons to a large bowl, fill with ice water and let stand 10 minutes.
Meanwhile, combine the cucumber and shallot in a colander, sprinkle with salt and let drain, 10 minutes. Whisk the peanut butter, soy sauce, mirin, rice vinegar, sesame oil, Sriracha, brown sugar, lemon juice and garlic in a small bowl.
Drain the carrots, blot dry with paper towels and transfer to a serving bowl. Press the cucumber and shallot in the colander with your hands to remove any excess liquid; pat dry with paper towels and add to the carrots. Add the mint and basil and toss to combine. Drizzle the peanut dressing over the salad and sprinkle with the sesame seeds.