Heat the olive oil in a skillet over medium-high heat. Stir in the minced shallot, morel and oyster mushrooms; cook until the mushrooms have lightly browned, and are soft. Pour in the white wine, and cook until evaporated. Scrape the mushrooms onto a plate, and set aside to cool. Meanwhile, stir together the cumin, paprika, oregano, brown sugar, garlic powder, parsley flakes, pepper, and salt in a bowl. Coat the lamb rack with the spice mixture and set aside.

Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with aluminum foil and lightly grease.

Spread the mushroom mixture evenly over one side of the puff pastry. Cut a slit 2 inches away from one edge of the puff pastry for each bone on the lamb rack. Carefully poke the bones through the slits and wrap the pastry around the lamb rack, pressing the edges of the pastry together to seal. Place onto the prepared baking sheet and brush with the beaten egg yolk. Refrigerate the lamb for 10 minutes before baking.

Bake the lamb in the preheated oven until the pastry has puffed and turned golden-brown, about 15 minutes. Remove, and let rest for 5 minutes before slicing. While the lamb is resting, bring the demi-glace to a simmer in a small saucepan. Whisk in the butter until dissolved. Drizzle the demi-glace over the sliced lamb chops, and sprinkle with chopped fresh parsley to garnish.