Combine tomatillos and next 4 ingredients in a saucepan. Bring to a boil, reduce heat, and simmer about 30 minutes.
Pour mixture through a wire-mesh strainer into a container, reserving 1/2 cup liquid. Place tomatillo mixture and reserved liquid in a blender. Add avocado, cilantro, and lime juice; process until smooth. Transfer to a saucepan, and heat until warm. Gradually whisk in butter, salt, and pepper until well blended.