Step 1

Bring a medium saucepan of water to a boil. Add the potatoes and cook over moderately high heat until tender, about 10 minutes. Drain and slice the potatoes crosswise 3/4 inch thick.

Step 2

In a large nonstick skillet, heat the oil until shimmering. Add the potato slices and cook over moderately high heat, turning occasionally, until lightly browned, about 5 minutes. Season with salt and pepper. Add the chorizo and ham and cook over moderately high heat, stirring occasionally, until the ham is crisp, about 2 minutes. Stir in the piquillo peppers and cook for 1 minute.

Step 3

In a medium bowl, beat the eggs with a generous pinch of salt and pepper. Add them to the skillet and use a rubber spatula to scrape and stir until large, soft curds form, about 5 minutes. Stir in the Manchego and cook, stirring, just until melted, about 30 seconds. Transfer the eggs to a platter, sprinkle with smoked paprika and serve.