How to Make It
In a medium bowl, toss the shredded carrots with the garlic, vinegar, 1/2 cup of the cilantro and 1/4 cup of the grapeseed oil. Season the carrots with salt and pepper. Let the carrots stand for 15 minutes; drain well.
Meanwhile, in a small saucepan, boil the carrot juice over moderate heat until it is reduced by half, about 5 minutes. Let the reduced carrot juice cool slightly, then transfer to a bowl. Whisk in the mayonnaise, sesame oil, ginger juice and the remaining 1/4 cup of grapeseed oil. Season the carrot dressing generously with salt and pepper.
Add the carrot dressing and the remaining 1/2 cup of cilantro to the carrots and toss the salad well. Transfer to a shallow bowl and serve immediately.
To make ginger juice, puree peeled and chopped fresh ginger in a food processor, then press the puree through a fine sieve.