1. In a large saucepan, combine 1 cup of the stock with the cider, shallots, bay leaves and sherry vinegar. Boil over high heat until reduced by half, about 25 minutes. Add the heavy cream and nutmeg and simmer over moderate heat until slightly thickened, about 5 minutes. Remove from the heat.
2. In a medium saucepan, heat the vegetable oil. Add the onion and cook over moderate heat until softened. Add the remaining 1 cup of stock and the chestnuts and simmer until the liquid reduces by a third, about 4 minutes. Remove from the heat and add the maple syrup and butter. Transfer the contents of the saucepan to a blender and puree until smooth. Blend in the crÃ¨me fraÃ®che. Transfer the puree to a clean saucepan and season with salt and pepper. Cover and keep warm.
3. Gently reheat the nutmeg vinaigrette. Add the scallions and parsley and season with salt and pepper.
4. Cut the lobster tail meat into 1-inch chunks and replace it in the tail sections of the lobsters. Spoon half of the chestnut puree in the center of each of 2 large platters. Arrange the lobster halves around the puree. Spoon the warm nutmeg vinaigrette over the lobsters, garnish the platters with the greens and serve at once.
MAKE AHEAD: The recipe can be prepared through Step 2 and refrigerated overnight. Finish the vinaigrette and rewarm the chestnut puree before serving.