Preheat oven to 300°. Cut half a potato into about 1/8-in.-thick slices. Heat 1 tbsp. oil in a seasoned 10-in. cast-iron skillet or ovenproof nonstick frying pan over medium-low heat. Add a layer of potatoes and sprinkle with some salt and pepper. Cook, turning once, until potato slices are just tender and only barely browned, 5 to 8 minutes. Transfer from pan to a plate. Repeat cutting and cooking with half a potato at a time, salt, and pepper, adding additional oil as needed.
Add 1 more tbsp. oil to pan and increase heat to medium. Layer all the potatoes in pan; pour eggs on top. Cook until underside is golden, 3 to 5 minutes.
Bake until eggs are set when pan is shaken, about 20 minutes. Let tortilla stand at least 10 minutes. Loosen from pan with a flexible spatula. Gently invert tortilla onto a platter or board. Sprinkle with parsley. Cut into wedges and serve warm or at room temperature with romesco.
Make ahead: Up to 3 hours; serve at room temperature.
Dominick's, Little Dom's, the 101 Coffee Shop, and Tom Bergin's, all in Los Angeles