Heat oven to 400° F.
Heat 1 tablespoon of the oil in a large ovenproof skillet over medium heat. Add the yellow onion and cook for 5 minutes. Add the chorizo, potatoes, 1/2 teaspoon salt, and 1/2 teaspoon pepper and cook, covered, stirring occasionally, until the potatoes are tender, 10 minutes. Stir in the parsley.
Pour the eggs into the skillet and stir to distribute the ingredients. Sprinkle with the Manchego and transfer to oven.
Bake the omelet until puffed and brown around the edges and a knife comes out clean, about 15 minutes.
Divide the lettuce and red onion among individual plates and drizzle with the remaining oil. Cut the omelet into wedges and serve with the salad.
Tip: This Spanish omelet is delicious served cold as an hors d'oeuvre. Use a cookie cutter or a shot glass to cut one into bite-size pieces.