Melt butter in a large pot over medium heat. Add potatoes and onion. Cook, stirring constantly, until tender but not brown, about 5 minutes. Increase heat to medium-high and add chicken. Cook until chicken is white, 7 to 10 minutes. Add water and bring to a simmer. Add corn and bring soup to a simmer again.
Season soup with salt and pepper. Add milk and mozzarella cheese.