Bring cauliflower and chicken broth to a boil in a large saucepan over high heat. Reduce heat to medium, cover, and simmer for 10 minutes. Uncover the saucepan and increase heat to medium-high. Allow cauliflower to simmer until soft and the cooking liquid has reduced by half, about 10 minutes.
Remove cauliflower from the heat, and add the butter, Cheddar cheese, and Parmesan cheese. Mash with a potato masher until the cheeses have melted and the cauliflower is smooth, then season to taste with salt and pepper.