Method

1. Soak 1/3 cup small pearl tapioca in 1 cup of milk for 1 hour.
2. Shuck 16 oysters. Trim away the muscle and the outer ruffled edge of each oyster and place the trimmings in a saucepan. Reserve the whole trimmed oysters and strain the oyster juice into a separate bowl.
3. Whip 1/2 cup of cream just until it holds its shape and store in the refrigerator
4. Drain the softened tapioca in a strainer and discard the milk. Rinse the tapioca under cold running water, then place it in a small heavy pot.
5. Pour 3/4 cup milk and 3/4 cup cream over the oyster trimmings. Bring to a simmer, then strain the infused liquid onto the tapioca.
6. Cook the tapioca over medium heat, stirring constantly with a wooden spoon, until it has thickened and the spoon leaves a trail when it is pulled through, 7 to 8 minutes. Continue to cook for another 5 to 7 minutes, until the tapioca has no resistance in the center and is translucent. Remove the pot from the heat and set aside in a warm place.
7. Place 4 large egg yolks and half the oyster juice in a metal bowl set over a pan of hot water. Whisk vigorously over medium heat for 2 to 3 minutes to incorporate as much air as possible. The finished sabayon will have thickened and lightened, the foam will have subsided, and the sabayon will hold a ribbon when it falls from the whisk. If the mixture begins to break, remove it from the heat and whisk quickly off the heat for a moment to recombine, then return to the heat.
8. Stir the hot sabayon into the tapioca, along with a generous amount of black pepper. Mix in 1/4 cup of crème fraîche and the whipped cream. The tapioca will be a creamy pale yellow with the tapioca pearls suspended in the mixture. Season lightly with salt, remembering that the oysters and the caviar garnish will both be salty. Immediately spoon 1/4 cup tapioca into eight gratin dishes. Tap the gratin dishes on the counter so that the tapioca forms an even layer. Cover and refrigerate until ready to use, or for up to a day.
9. Preheat the oven to 350º F.
10. Combine 3 tbsp vermouth, the remaining reserved oyster juice, 1½ tbsp minced shallots and 1½ tbsp vinegar in a small saucepan.
11. Simmer until most of the liquid has evaporated. Whisk 8 tbsp chilled butter piece by piece.
12. Meanwhile, place the dishes of tapioca on a baking sheet and heat in the oven for 4 to 5 minutes, or until they just begin to puff up.
13. Add the oysters and some chopped chives to the sauce to warm through.
14. Spoon 2 oysters and some of the sauce over each gratin and garnish with caviar. Serve immediately.