Place potatoes in a pot, cover with 1 inch of water, stir in 1/2 tsp. salt and bring to a boil. Reduce heat and simmer until tender, 5 to 7 minutes. Drain.
Warm oil in a 10-inch ovenproof nonstick skillet over medium-high heat. Add onion and cook, stirring often, until tender, about 3 minutes. Add bell pepper and chorizo and cook, stirring often, until pepper is softened, 3 to 5 minutes. Stir in potatoes, season with salt and cook, stirring occasionally, until potatoes begin to brown, about 5 minutes.
Press lightly on mixture so it forms a cake. Reduce heat to medium and continue to cook until golden and crisp on bottom, 5 to 7 minutes.
Preheat broiler to high. Carefully break eggs onto potato cake, then place pan under broiler and cook until whites are set, about 2 minutes. Sprinkle with cilantro and serve.