In a nonstick skillet, melt 2 tablespoons butter over medium heat. Add the apple, onion and celery; season with the poultry seasoning, and salt and pepper to taste. Cook, stirring occasionally, until the onion is tender, 5 to 6 minutes. Transfer to a bowl and let cool for 5 minutes. Wipe the skillet clean and return it to the stove.
Preheat the broiler. Add the turkey and parsley to the apple mixture, season with salt and pepper and combine with a fork; form into four 4-inch patties. In the skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Cook the patties for about 6 minutes on each side, lowering the heat for the last 2 or 3 minutes.
While the burgers cook, mix the cranberry sauce, orange zest and scallions. Toast the English muffins under the broiler, then remove and spread lightly with the remaining 1 tablespoon butter.
Place the burgers on the buttered English muffin bottoms, and top with the lettuce, lots of cranberry relish and the buttered tops.