Make the Five-Minute Eggs: In a small saucepan, bring 4 cups of water to a boil. Add the eggs, reduce the heat, and simmer for 5-6 minutes, depending on the size of the eggs. Run the eggs under cold water, peel, and halve; the eggs should have nice golden, creamy yolks.
On a large plate, spoon dollops of Romesco Sauce, then nestle in the egg halves. Finish with a dab of Romesco, a drizzle of olive oil, a sprinkle of sea salt, and a parsley leaf or two.