Heat a medium nonstick skillet over medium heat. When it is hot, sprinkle half of the cheese evenly over the bottom of the skillet. Cook, shaking pan occasionally to assure an even distribution of cheese over the pan bottom, until the edges are lacy and toasted, about four minutes.
Remove pan from heat and allow cheese to set for about 30 seconds. Use a large heatproof spatula and tongs to carefully flip frico over and cook until the other side is golden, another two minutes. Slide frico out of the pan and onto a paper towel-lined plate. Repeat with remaining cheese and let stand while you prepare the eggs.
Cut chorizo into half-inch dice. Heat a nonstick skillet to medium-high heat and add chorizo. Once the fat from the chorizo has started to render, after about a minute, add onion and stir. Reduce heat to medium and cook, stirring often, until onion is soft and onion and chorizo have browned slightly. Pour off all but 1 tablespoon of the fat.
Whisk eggs to break up yolks and add to skillet. Add parsley to taste. Reduce heat to low and cook, stirring and scraping the bottom often (this yields a soft, fluffy texture). Spoon scrambled onto plates and season to taste with pepper and salt (keep in mind that fricos are salty and chorizo is peppery). Break fricos into approximately 3-inch pieces and serve with eggs.