Melt 1 tablespoon butter with half the olive oil in a large sauté pan or skillet over medium heat. Add the onion and apple and cook, stirring frequently, until very tender. Transfer to a blender or food processor.
Add the remaining oil and another tablespoon butter to the pan and heat over high heat. Add the livers and sauté quickly until very pink in the center but not rare. Using a slotted spoon, add the livers to the onion mixture. Pour the Calvados into the pan, simmer a minute or two, scraping loose the browned bits, and add to the livers. Cut the remaining ½ cup butter into slivers and add it with the cream to the livers. Process until very smooth. If there are any lumps, press the puree through a strainer. Season to taste with salt and pepper and add more Calvados if desired.
Line the bottom of a 9 by 5-inch glass loaf pan with baker’s parchment and butter the paper and sides of the pan. Pour in the mousse and spread evenly. Pour the clarified butter over the top. Cover with plastic wrap and refrigerate overnight or up to 2 days. (The mousse can also be made in buttered ramekins. Occasionally this pâté refuses to set up enough to unmold, so that ramekins are the most foolproof means of serving.)
To serve, dip the bottom of the pan in hot water, then invert the mousse onto a platter. Cut into slices and serve with croutons, apple slices, and some greens tossed with a little Walnut Vinaigrette, or simply with toast or croutons.