Heat ¼ cup of the olive oil over medium in a cast iron skillet large enough to accommodate 16 poached eggs. (If you don't have a skillet that large, use two pans, dividing the ingredients evenly between them.) Add the onions, bell peppers, garlic, dried lime (if using), paprika, cumin, coriander, and salt and cook, stirring occasionally, until the vegetables haven softened but not browned, about 10 minutes. Add the tomato puree and sugar and simmer until reduced by about one-third, 10 to 12 minutes. Whisk in the remaining ¼ cup oil. Crack the eggs into the skillet, spacing them evenly in the sauce. Lower the heat, cover, and cook until the egg whites are set but the yolks remain runny, about 5 minutes. Top with serrano chiles and cilantro and serve immediately right from the pan.