In a medium sized bowl, combine the butter, chipotle chiles, tarragon and salt, using a spatula to press the ingredients together until evenly blended. Place the butter in the refrigerator to firm back up while preparing the other ingredients.
In a separate small bowl, prepare the gremolata by combining the parsley, lemon zest and garlic. Set aside.
Preheat a grill on medium high. While the grill is heating up, shuck the oysters, being careful to avoid getting grit in the shell. Discard the flat side of the shell, leaving the oysters in the rounded cup side. Line up the oysters on a baking sheet.
Top each oyster with approximately 1/2 - 1 tablespoon of the chipotle-tarragon butter. The exact amount will depend on the size of the oyster and shell.
Carefully place each oyster directly on the grill and close the lid. Cook for 3-4 minutes (note: it’s better to undercook than overcook the oysters. The idea here is to let them fry for a bit in the butter and get a smokey flavor from the grill).
Use tongs to very carefully remove the oysters from the grill and place back on the baking sheet. Depending on the shape of the shells, hot butter will likely spill from a couple of them (but the flavors will stay!)
Sprinkle a small amount of the gremolata over each oyster and serve immediately.
Save any leftover gremolata! It's an excellent condiment to serve over meat, seafood, pasta or vegetables.Recipe inspired by Chef Nate Lindsay