Preheat the oven to 400°F.
Cut 8 4.5-inch rounds from the pastry.
Cut 3.5-inch circles in the center of four of the 4.5-inch rounds; place each outer ring atop one of the remaining 4.5-inch circles and set them aside.
Reserve the 3.5-inch disks for another use (I made strawberry tartlets).
Bake on a Silpat® or parchment-lined baking sheet for 18-22 minutes, or until puffed and golden.
Set aside to cool.
With a very sharp paring knife, cut around the raised rim to create the tops of the sarcophagi. Be careful to take only the top layer of the pastry as shown in the photos.
Raise the oven to 450°F.
Season the inside of the quails with some salt and a few grinds of pepper.
Mash the pâté and divide into 8 pieces; form each piece into a lozenge-shaped disc.
Using a truffle slicer or very sharp knife, cut 12 slices from one of the truffles
Lay 3 slices of truffle on each of 4 pâté disks.
Cover them with the remaining disks of pâté and stuff into the cavity of each quail.
Truss the quails.
Slice remaining truffle and set aside.
Season the outsides of the quail with salt and a few grinds of white pepper.
Melt 1 tablespoon butter in an ovenproof skillet over high heat.
Sear the quails, starting breast-side up, for 20 to 30 seconds per side.
Place the pan in the oven (with quail breast-side down) and roast for 8 minutes.
Turn the quails breast-side up and roast for 5 minutes more. Remove quail to a plate; cover and keep warm.
Place the skillet over high heat on top of the stove.
Pour in the Madeira and bring to a boil, scraping up any browned bits on the bottom of the pan with a wooden spoon.
Simmer for 1 minute.
Pour in the demi-glace and reserved truffle slices and simmer for 2 minutes or until the sauce is reduced and coats the back of a spoon.
Stir in the remaining tablespoon butter, and season with salt and pepper to taste.
To serve, put each quail in a pastry nest, and drizzle with sauce, spooning sauce around the sarcophagi, as well.