Preheat oven to 350F.
Combine butter, garlic, shallot, oregano, parsley, lemon zest and juice in a food processor. Pulse to combine.
Pat turkey or chicken dry and arrange on a cooling rack set over baking sheet so the heat circulates around the meat as it roasts. Smear skin with butter and sprinkle with salt and pepper. Roast 45 minutes, to an internal temp of 170F, until skin crisp and brown. Cover with loose foil and rest 10 minutes before carving.
Meanwhile, cover potatoes with cold water in a large pot and bring to a boil. Salt water and cook to tender, drain and return to pot. Add 2 tablespoons lemon-herb butter, 1/2 cup stock, EVOO, feta and olives, and mash. Season with salt and pepper, to taste. Reserve covered.
Melt remaining lemon-herb butter in a skillet over medium heat. Whisk in flour, cook 1 minute then whisk in remaining stock, about 1 1/2 cups. Cook to thicken, season with Worcestershire, salt and pepper. Temper egg yolk with some of the gravy then return to sauce to add gloss and deepen the gravy's smooth finish.
Slice turkey or chicken and serve with mashed potatoes and gravy.