Combine potatoes, onion, turkey, ham, celery, carrots, asparagus, peas, and butternut squash in a large pot. Pour chicken broth and water over mixture; bring to a boil. Reduce heat to medium and simmer soup until potatoes and squash are tender, 10 to 15 minutes. Stir Italian seasoning, white pepper, salt, and bay leaves into soup and continue to simmer.
Melt butter in a saucepan over medium-low heat. Whisk flour into butter, whisking constantly, until thickened, about 1 minute. Slowly stir milk into flour mixture until mixture it smooth and thickened, 4 to 5 minutes. Stir milk mixture into soup and cook until thickened and heated through, 3 to 5 minutes.
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