Make the mignonette sauce by combining the vinegar, shallots, and salt and pepper in a small bowl. Cover and refrigerate until needed.
Scrub the oysters in cold water. Place an oyster, cupped-side down with the pointed end facing you, on a slightly damp kitchen towel. Hold it in place with another kitchen towel. Insert the point of an oyster knife into the hinge of the shells. Work the knife in 1/4 inch, and then twist it to pry the oyster open. Slide the knife across the top shell and remove. Slide the knife under the oyster to detach it from the bottom shell. Remove any shell fragments. Repeat with remaining oysters.
Serve the oysters with the mignonette sauce. For super-chilled oysters, serve them on a bed of crushed ice.