Place a roasting pan large enough to hold the lobsters in the oven and preheat to 450 degrees. With the tip of a sharp knife pierce lobsters between the eyes to sever the spinal cord. Crack claws using the blunt edge of a cleaver or a hammer. Place lobsters in the hot roasting pan, drizzle with oil and roast until red, about 15 minutes. Remove from oven, and set aside.
Melt 2 teaspoons of butter in a small sauce pan, add the shallots and sauté over low heat until soft and translucent, about 3 minutes. Add wine and vinegar, raise heat and cook at a moderate boil until the liquid is reduced to 1 tablespoon, about 5 minutes. Remove the pan from the heat, and whisk in 6 tablespoons of butter, about 1 tablespoon at a time until all is incorporated. Scrape the seeds from the vanilla bean into the sauce, stir to combine and strain out the shallots through a chinois (strainer) into a clean saucepan. Use a spoon or wooden spoon to gently mash the shallots in the chinois to squeeze out all of the sauce. Season with ¼ teaspoon salt and pepper, and set aside.
When the lobsters are cool enough to handle, remove the meat from the claws. Detach the tails, and discard the heads. With a pair of scissors, cut the shell on the underside of each tail in half lengthwise, remove the meat and cut into ¼-inch-thick slices. Loosely cover the meat with aluminum foil, and keep warm.
Melt 1 tablespoon of butter in a large pot, and add spinach and Vidalia’s. Stir until greens have melted down, and continue to cook, stirring occasionally, until the greens become tender, about 5 minutes. Season them with ¼ teaspoon of salt and pepper.
To serve, reheat the sauce over low heat until warm, whisking constantly. Place a bed of greens on each plate, arrange the lobster meat on top and spoon the sauce over the lobster. Top with clover Sprouts. Serve immediately.