Heat a nonstick skillet over medium high heat. Add oil, 2 turns of the pan. Add chopped mushrooms and shallots and season with salt and pepper. Saute mushrooms 5 or 6 minutes until dark and tender. Remove from heat. Transfer mushrooms to a bowl and return pan to stove top to preheat to cook patties.
Add turkey to the mushroom mixture. Make a well in the center of the meat. Add sage, Worcestershire sauce, bread crumbs and beaten egg and season with salt and pepper. Mix turkey meat loaf and make a small 1-inch patty. Place meat in the hot pan and cook 1 minute on each side. Taste the mini patty to help you adjust seasonings. Divide meat loaf mixture into 4 equal parts by scoring the meat before you form patties. Form 4 equal oval patties 1 inch thick. Add 1 tablespoon extra-virgin olive oil, 1 turn of the pan, and arrange patties in the skillet. Cook 6 minutes on each side and transfer to a serving plate or individual dinner plates. Return pan to heat and add butter. When butter melts, whisk in flour and cook 1 to 2 minutes. Whisk in stock and season gravy with poultry seasoning, salt and pepper, to taste. Simmer gravy until it reaches desired thickness, and pour over patties, reserving a little to pass at the table.
Clean mushrooms with a damp cloth. Do not run directly under water.