In a food processor, pulse butter with green onion, oregano and coriander until smooth.
Gently peel away husk of corn and pull off silk. Rub each ear generously with herb butter. Fold back husks to cover corn, tie tops of husks with twine and chill for at least 20 minutes, up to a day.
Preheat grill to medium high and grill corn for about 18 minutes, turn occasionally to cook evenly. Serve corn in the husk and allow guests to peel, sprinkle with grated Parmesan and eat.