Preheat the broiler. Add the shallot, ginger, and cloves to a small bowl. Whisk in the vinegar. Add the olive oil, season with salt and pepper, and whisk until combined.
Place the oysters on a large baking sheet. Spoon the vinegar mixture on top of the oysters. Put in the oven and broil for 3 minutes. Remove from the oven.
Arrange the oysters on a large serving plate. Serve immediately with the lemon wedges.