Heat the broiler to high. In a small roasting dish or toaster pan, roast the tomatoes for 10 to 12 minutes on the highest rack, until they’re blackened in places.

Spread enough rock salt onto a baking sheet to make a layer into which oysters will firmly sit. While the tomatoes are roasting, shuck the oysters by holding a dish towel in your nondominant hand, and holding the oyster around its rounded tip, with its cup side down, on a counter, then inserting an oyster knife into its hinge, wiggling it in entirely until the hinge gives, and then moving it around. (Even better, watch our video on how to shuck, several times, and then approach the task confidently.) Detach each oyster from its bottom shell. As each is done, secure it in a little well in the rock salt, so that it retains its oyster liquor.

Leaving the broiler on high, combine the roasted tomatoes with the butter in a blender or food processor or with an immersion blender or with a lot of elbow grease. The resulting mixture will be mottled and ugly but will melt to glossy perfection. Stir in the shallot.

Place a 1/2 teaspoon dollop of tomato butter into each oyster. Place the tray into the oven, and broil until the tomato butter is melted and the oyster is beginning to darken and curl around its edges, around 8 to 12 minutes. Serve very hot, immediately.