Heat 2 tablespoons of oil in a nonstick skillet. Cook sausage until golden brown and cooked. Remove from pan and drain on a paper towel. Add 2 additional tablespoons of oil to the pan; cook potatoes and onions for 2 to 3 minutes, turning frequently. Cover tightly and cook over a gentle heat for about 30 minutes, turning occasionally, until softened and slightly golden.
In a mixing bowl, combine beaten eggs with parsley, cheese, sausage, and plenty of seasoning. Gently stir in cooked potatoes and onions until well coated, taking care not to break up potato slices. Wipe skillet with paper towel and heat the remaining 2 tablespoons of oil. Add potato mixture to the pan and cook over a very low heat until egg begins to set. Use a knife along the edge of the pan to prevent the tortilla from sticking to the sides.
Preheat broiler. When the base of the tortilla has set, protect the panhandle with foil and place under the broiler until the tortilla is set and golden brown. Cut into wedges.