Melt the butter over medium heat in a small saucepan. Add the shallots and cook, stirring, until they are translucent and beginning to soften, about 2 minutes. Add the chardonnay, bring to a lively simmer, and reduce until only about 2 tablespoons of liquid remains. Add the cream and bring to a boil. Lower the heat to a simmer and reduce to 2/3 cup. Remove from the heat, stir in the white pepper, and set aside.
Preheat the oven broiler to 500 degrees F. Arrange the top oven rack so a roasting pan will fit below the heating element. Prepare appetizer plates by placing a bed of rock salt on each, to hold the oysters. Distribute the rock salt evenly between to roasting pans large enough to hold the oysters.
If the fishmonger shucked your oysters, return the oysters to their cleaned shells one by one, and add about 1/2 teaspoon of the oyster liquid to each, nesting the shells carefully in the rock salt so the contents don't spill. Otherwise, arrange freshly shucked oysters in the rock salt-filled roasting pans, ensuring that their liquid doesn't spill.
Spoon about 2 teaspoons of the shallot-cream mixture on top of each oyster. Coat each oyster well, without having the shell overflow with liquid. Put one roasting pan in the oven and broil just until the liquid bubbles and the oysters' edges begin to curl, about 3 minutes, watching closely to prevent burning. Repeat with the other roasting pan. Carefully lift 4 oysters in their shells onto each appetizer plate. Serve immediately.