Using a blender puree tomatillos and chilies. Transfer pureed mixture to a skillet and add cream and shallot, cooking over medium high heat, stirring until thickened (4-5 minutes). Strain sauce. Over low heat whisk in butter 1 tablespoon at a time and season with salt. Keep warm.
In a barbecue, heat the mesquite charcoal and hickory chunks until coals are white. Add more hickory chunks. As soon as smoke rises, push coals and chunks to one side of barbecue. Oil grill well.
Arrange shrimp on side of grill not over heat source. Cover and smoke for 6-8 minutes or until shrimp is opaque.