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1
Combine the butter and chopped tarragon in a food processor and process until smooth.
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2
Add the black pepper and 1 teaspoon salt and pulse a few times to combine.
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3
Scrape the mixture into a bowl.
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4
Preheat a grill or the broiler to high or heat a grill pan over high heat.
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5
Spread 1 cup kosher salt over the bottom of a large platter.
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6
Combine the barbecue sauce and chile powder in a small saucepan and bring to a simmer over low heat.
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7
Keep warm.
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8
Carefully shuck the oysters over a bowl, reserving all of the oyster liquor.
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9
Return each oyster to its bottom shell; discard the top shells.
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10
Add some of the oyster liquor back to the oysters in the shell.
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11
Top each oyster with about a teaspoon of the butter.
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12
Carefully place the oysters in the half shell on the grates of the grill or on the grill pan.
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13
Cook until the sauce starts to bubble and the oysters are just cooked through, about 2 minutes.
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14
(Alternatively, you can place them on a baking sheet and heat under a preheated broiler for about 2 minutes.)
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15
Remove the oysters from the grill using tongs, place on top of the salt on the platter, and top each with a small spoonful of the barbecue sauce.
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16
Garnish with tarragon leaves and serve immediately.
