Bring a small pot of lightly salted water to a boil; cook kohlrabi cubes in boiling water until soft, about 15 minutes; drain.
Cook red potatoes in microwave oven until soft, about 10 minutes.
Beat kohlrabi, potatoes, and garlic scape together in a bowl with an electric hand mixer until smooth; transfer to a 1-quart casserole dish and top with mozzarella cheese.
Bake in the preheated oven until the cheese begins to brown, about 30 minutes.
