How to Make It
Pulse garlic and shallots in a food processor until finely chopped, 3 to 5 times. Add butter, parsley, sumac, salt, and cayenne pepper, and process until well combined, about 1 minute. Cover and chill for at least 1 hour.
Preheat grill to medium-high (400°F to 450°F). Arrange oysters in a single layer on grill; cover with wet burlap or towel. Grill oysters, covered, until oysters open, 10 to 12 minutes. Using tongs, carefully transfer roasted oysters to a platter.
Melt 1/2 cup of the garlic butter in small saucepan over medium. Remove and discard top shells from oysters, and spoon 2 teaspoons melted Garlic-Parsley Butter on each oyster. Serve immediately. Reserve remaining butter for another use.