Preheat grill or Great Grate over medium heat.
Scrub and rinse the oysters. Keep refrigerated until ready to grill.
To make the sauce: Pour the cream into a 1-quart saucepan and cook over low heat, whisking occasionally to prevent the cream from boiling over, until the volume is reduced by half, about 8 minutes. Increase the heat to medium and add the butter, 1 piece at a time, whisking constantly, until the sauce is shiny, emulsified, and thick enough to coat the back of a spoon. Add the lemon juice and simmer briefly. Remove the saucepan from the heat. Add the chervil or parsley and season, to taste, with salt and pepper. Keep the sauce warm until ready to serve.
Set up the oysters on the grill with the cup side down (and flat side up) or place them directly on the grill in the same fashion. Cook the oysters without turning them.
As soon as the oysters pop open, after 8 to 10 minutes, transfer them carefully with tongs to a platter (or plates) lined with a bed rock salt. If you are using a Great Grate, this won't be necessary. Use the tongs to pry off the top shells. Spoon 1 teaspoon sauce over each oyster and serve immediately.