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 for 2 minutes. Add broth, milk, and bay leaf; bring to a boil. Reduce the heat to low, cover, and simmer until kohlrabi is tender, about 25 minutes.

Remove and discard bay leaf. Blend soup with an immersion blender. Season with salt and pepper.

Add orzo, cover, and simmer until orzo is tender, about 10 minutes.