Peel tough parts off kohlrabi bulb and separate stems. Halve leaves lengthwise and then thinly shred crosswise. Julienne the kolhrabi in a food processor with a shredding blade (alternatively, use a veggie peeler that juliennes, or do by hand if you have time). Julienne the turnip also.

Whisk together the lime juice, peanut oil, honey, sesame oil, salt, and pepper. 

Add scallions, kohlrabi, turnip, and leaves to a bowl, toss to coat. Let stand at least 15 minutes.