Stir together the vinegar, lime juice, honey, onions, jalapeno, chopped herbs and some salt and pepper in a small bowl. Let sit at room temperature for at least 10 minutes to allow the flavors to meld.
Remove the tops of the oysters over a bowl, catching any of the oyster liquor that comes out. Add the liquid back to the bottom shell with the oyster. Put on the grill and grill until the liquid just begins to simmer but the oysters are still a little raw in the center, about 4 minutes. Carefully remove with tongs to a platter and top each oyster with a teaspoon of the mignonette.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.