Bone the chukar from the back, keeping the bird in one boneless piece. Remove the bones from the rear legs and reserve them for the farse.
Grind the chukar leg, foie gras, pork fat, and milk-soaked bread squeezed of its liquid with a medium die on the sausage grinder. Add the ground meat mixture, egg white, fig jam, sea salt, and quatre epices in a medium-sized bowl and mix thoroughly.
With the skin side down on your work surface, add farse to the entire meat surface. Roll the bird into a spiral, keeping the skin on the outside. Truss the bird with butcher twine, then season with cracked pepper and sea salt.
Blanch like-sized fingerling potatoes in salted water until tender. Drain and let cool. Smash potatoes with the palm of your hand. Place potatoes in a medium mixing bowl and dress with lemon zest, ½ of the chopped chives, sea salt, olive oil, and melted butter. Place potatoes on a lined sheet tray under the broiler until golden brown, then remove. Season the potatoes with parmesan cheese and reserve.
Dice porcini mushrooms. In a cast iron skillet, sear mushrooms and thyme in olive oil until golden brown. Add sliced garlic and sauté for an additional 2 minutes. Deglaze with sherry, add chicken stock, reduce by half, and reserve.
Toss purslane with lemon juice, olive oil, sea salt, and reserve.
Lightly brown chukar in olive oil, then place in a 350F-degree oven until it reaches 160F internal temperature. Let rest while finishing potatoes and mushrooms.
Place potatoes under the broiler for 2 minutes. Heat mushroom jus then and butter and reserve.
To plate, divide potatoes between two plates and top with remaining chopped chives. Slice chukar into six slices and shingle atop potatoes on each plate. Drizzle warm porcini jus atop the chukar and around the plate. Divide purslane evenly on both plates and season the sliced chukar with flaky sea salt.
