Preheat the oven to 400°F. (Alternatively, the oysters can be roasted on a gas or charcoal grill; preheat the grill for direct, high-heat grilling.)
If using the oven, line a rimmed baking sheet with
aluminum foil, scrunching up the foil into irregular
mounds to help hold the oysters in place. Place the oysters on the foil, cup-side down, arranging them so they are as flat as possible so none of their liquor spills out when the shells open. (If using the grill, place the oysters directly on
the grates once the grill is up to temperature.) Roast the oysters in their shells until the shells have begun to open and you can see some steam escaping, about 8 minutes.
While the oysters roast, make the zabaglione: In a medium bowl, whisk the cream until it holds soft peaks. Set aside.
Bring 2 inches of water to a simmer in a large saucepan. In a large nonreactive bowl, whisk together the egg yolks and wine. Season with salt and pepper. Set the bowl over the simmering water; make sure the bottom of the bowl is not
touching the water. Cook, whisking continuously, until the mixture has thickened and gained volume, about 4 minutes.
Remove the bowl from the heat. Whisk vigorously for another minute, then gently whisk in the grated
Parmigiano-Reggiano rind. Season with salt and pepper.
Gently whisk in one-third of the whipped cream to lighten the mixture, then add the remaining cream, whisking very gently to incorporate without overworking the sauce.
Remove the oysters from the oven. Preheat the broiler. Using an oyster knife, carefully remove and discard the top shells of each oyster, separating the meat from the shell and taking care not to spill the liquid in the bottom shell. Return the oysters (still in the bottom shell) to the baking sheet and
spoon some zabaglione over each. Place under the broiler
and broil just until the zabaglione has a hint of color, 1 to 2 minutes. Carefully transfer to a serving platter and garnish with the chives. Serve immediately.