Preheat oven to 375°F. Wrap garlic head in aluminum foil, and bake in preheated oven until garlic cloves are soft and golden, about 40 minutes. Let cool until cool enough to handle, about 30 minutes. Squeeze cloves out gently.
Process butter, parsley, tarragon, shallot, lemon zest, salt, pepper, and 2 tablespoons of the roasted garlic in a food processor until smooth. Chill until ready to use.
Heat grill to medium-high (about 450°F). Melt butter mixture in a small saucepan over medium. Reduce heat to low, and keep warm while preparing the oysters.
Grill oysters, covered, until oysters open, 8 to 10 minutes. Transfer oysters to a serving platter, and let stand until cool enough to handle with a towel, about 10 minutes. Pry open oysters, and place oysters on the half shell on the platter. Discard top shells. Drizzle warm melted butter mixture over oysters. Serve immediately.
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