Put the pancetta in a cast-iron skillet and cook over medium-high heat until crisp and the fat is rendered. Remove to a paper towel-lined plate.
While the pancetta cooks, combine the vinegar, shallots, peppercorns, basil, tomatoes and season with salt.
Prepare the charcoal grill using a chimney starter filled with charcoal briquettes. When the coals are red hot and begin to turn grey, add the soaked wood chips evenly over the top of the coals.
Grip each oyster, flat-side up, in a folded kitchen towel. Find the small opening between the shells near the hinge and pry it open with an oyster knife. Try not to spill the delicious juices, known as the oyster liqueur, in the bottom shell. Cut the oyster meat loose from the top shell, and then loosen the oyster from the bottom shell by running the oyster knife carefully underneath the body. Discard the top, flatter shell, keeping the oyster and juices in the bottom, deeper shell.
Brush the cooking grates clean. Grill the oysters over direct high heat until the juices start to bubble and the edges of the oyster curl, 2 to 4 minutes.
Spread 1 1/2 cups kosher salt evenly over the bottom of a large platter. Carefully nestle the cooked oysters in the salt and top each oyster with some of the mignonette, a few cubes of pancetta and some parsley leaves. Drizzle with a little extra-virgin olive oil.
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