Step 1Heat the oven to 400 degrees. Line a large baking sheet with paper towels and set it aside in a warm spot.
Step 2Combine the pistachios, flour, salt and cayenne in a shallow dish and mix well. Whisk the milk, egg white and mustard together in a second shallow dish.
Step 3Heat 2 tablespoons of oil in each of two large nonstick, ovenproof skillets over medium-low heat. Dip the skin side of each quail into the milk mixture, then lay each into the pistachio mixture to coat, pressing the quail in so that nuts adhere, especially to both sides of the legs. Carefully lay the quail crust side down into the hot oil and cook for 3 minutes, until lightly browned. Using tongs, carefully turn the quail over.
Step 4Transfer the skillets to a hot oven. Roast until juices run clear when the legs are pierced with a skewer, 3 to 5 minutes depending on the size of the quail. (Cook less time if you like pinker quail, longer for well done.)
Step 5Carefully remove the quail to the prepared baking sheet and keep warm. Return the skillets to the stove top over medium-high heat and divide the demi-glace and crushed peppercorns between them. Bring to a simmer, stirring.
Step 6Spoon a little of the sauce onto each of 4 to 8 serving plates and lay the quail on top. (Pass any remaining sauce on the side.) Serve at once.