Rinse mussels under cold water. Remove any hairy "beards" from the edge of the shells, then scrub with a vegetable brush. Discard any mussels with cracked shells, or which do not close when tapped firmly on the counter.
Heat oil in a large pot with a tight cover. Add garlic, scallions, shallot and a pinch of salt. Sweat aromatics until soft, about 3 minutes. Add corn and cook until beginning to soften, another 3 minutes.
Add sherry and bring to a simmer; maintain simmer until corn is cooked through, about 5 minutes. Add mussels and cover pot. Steam, stirring once or twice, until mussels are cooked through, 5-10 minutes. Discard any which do not open. Remove mussels to warmed bowls with a slotted spoon.
Add butter to pan juices and simmer until butter melts and sauce thickens slightly, about 2 minutes. Pour sauce over mussels and serve.