Cook onion and garlic in butter in a 5- to 6-quart heavy pot over moderately low heat, stirring, until softened, 3 to 5 minutes.
Add wine and mussels and cook, covered, over moderately high heat until mussels just open wide, 6 to 8 minutes. (Discard any mussels that have not opened after 8 minutes.)
Transfer mussels with a slotted spoon to a serving bowl, then transfer cooking liquid to a blender along with cream, basil, and pepper and blend until smooth (use caution when blending hot liquids). Season sauce with salt and pour over mussels.