Cook the carrots using your desired method. Add the melted butter and mash with a potato masher or fork until nearly smooth. (I like the texture it has when I left chunks of slightly unmashed carrot in the mix.)
Gently and carefully fold the egg white into the carrot mixture. Spoon into a 1 quart casserole or souffle dish that has been lightly greased or sprayed with butter-flavor cooking spray.