Melt butter in a large stockpot over medium-low heat. Cook and stir onion in melted butter until soft, about 10 minutes. Add kohlrabi; cook and stir another 2 minutes. Pour vegetable broth and milk over the onion mixture. Add bay leaf. Bring the mixture to a boil, place a cover on the pot, and reduce heat to low; cook at a simmer until kohlrabi is tender, about 25 minutes.
Remove and discard bay leaf; allow the soup to cool slightly. Pour the soup into a blender, filling the pitcher no more than halfway. Pulse the blender a few times before leaving on to puree. Work in batches until all soup is blended. Return pureed soup to stockpot; season with salt and pepper. Sprinkle orzo pasta into the soup; cover the stockpot and simmer until the orzo is tender, about 10 minutes.