The setMooshroomType function has private access in the MooshroomEntity class. This makes it impossible for a modded item or entity to either change the Mooshroom type or spawn a brown Mooshroom as far as I know. Other mobs like Rabbits and Horses have a similar function that has public access. This function is set to private in Vanilla Minecraft, but it would be nice to be able to access the function with mods.