First, make the champagne mignonette. It's best to make the mignonette a few hours before you are going to grill the oysters to allow it to cool and thicken appropriately. In a small bowl, combine 2 tablespoons champagne vinegar, 2 teaspoons finely chopped red onions, 1/4 teaspoon extra virgin olive oil, a pinch of granulated sugar, a pinch of coarse black pepper and a pinch of kosher salt. Gently stir ingredients together, before covering with plastic wrap and allowing to chill in the fridge for at least 2 hours.
Once the champagne mignonette is ready, prepare your oysters. Prepare a grill for medium-high heat. Place each oyster cupped side down on grate, cover grill, and grill until oysters begin to open. The oysters can take anywhere between 2 to 5 minutes, and will likely pop open only a quarter of an inch or less.
Transfer opened oysters to a platter, making sure to discard any that do not open. Let cool slightly (having a bed of ice to cool the oysters on allows you to handle the hot shells more easily), then use a short, blunt knife to pry the shells fully open, keeping cupped side down and retaining as much liquid as possible. Use a paring knife to cut the muscles connecting oysters to shells. Serve immediately.