Rub chicken legs with 1 tablespoon salt, and place in a bowl. Sprinkle with pepper and remaining salt. Add tea leaves. Refrigerate covered, turning chicken occasionally, for 10 to 12 hours, depending on how strong a salt cure is desired.
Preheat oven to 300 degrees. Rinse chicken under cool running water, and pat dry. In a skillet over medium heat, place chicken skin side down; cook until fat renders and skin browns, 15 to 20 minutes.
Transfer meat and reduced fat to a small casserole, placing chicken skin side up in one layer. Add enough olive oil to cover. Cover casserole with a lid, and place it in the oven. Cook until chicken has rendered all of its fat and the meat is falling from the bone, 2 to 2 1/2 hours.