Preheat oven to 350°F.
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 170°F, 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.