Preheat oven to 325°F. Place the oil in a very large skillet set over medium-high. Season the pork with salt and pepper. Sear the pork, in batches, on both sides. Set the pork in a large casserole dish, overlapping each piece.
Reduce the heat under the skillet to medium. Add the leek and garlic cook until tender, about 5 minutes. Mix in the flour and tarragon and cook 2 minutes more. Slowly, while constantly mixing, add 1 cup of the stock. When very thick, add the remaining stock, and the lemon juice and zest. Bring to a simmer. Season sauce with salt and pepper; pour over the pork. Cover and bake 90 to 105 minutes, or until pork is very tender. Sprinkle pork with green onion and serve.