Shave the daikon into ribbons with a vegetable peeler. Toss with 1/4 teaspoon salt in a colander; let drain in the sink, tossing occasionally, about 15 minutes. Meanwhile, shave the carrots into ribbons with the peeler.
Make the dressing: Whisk the ginger, vinegar, lime juice and 1/2 teaspoon salt in a large bowl. Slowly whisk in the vegetable oil and sesame oil until blended.
Toast the sesame seeds in a skillet over medium heat, tossing occasionally, until the white seeds are golden, about 5 minutes. Add 1 tablespoon seeds to the dressing.
Toss the daikon and carrots with the dressing and season with salt. Top with the remaining sesame seeds.
Photograph by Con Poulos
Recipe courtesy Food Network Magazine