Heat oven to 400°. On a rimmed baking sheet, toss potatoes with 1 tbsp of the oil, 1/4 tsp of the salt and 1/8 tsp of the pepper. Roast at 400° for 15 minutes, flip and roast another 10 minutes.
In a 10-inch nonstick skillet, cook chorizo 5 minutes over medium heat. Remove to a plate with a slotted spoon. Pour in remaining 1 tbsp oil. Add onion; cook 5 to 7 minutes, until softened. Stir in potatoes and chorizo. Reduce heat to medium-low.
In a bowl, beat eggs with remaining 1/2 tsp salt and 1/4 tsp pepper. Pour over mixture in skillet. Cook 10 minutes, then cover with foil. Cook 20 minutes, then loosen with a silicone spatula, place a plate on top of skillet and carefully flip tortilla onto plate. Slide tortilla back into skillet, uncooked side down. Cook another 5 minutes.
Flip onto a new plate, garnish with parsley and slice into 4 pieces.