Heat the oil in a large skillet over medium. Add the onion and poblano; cook, stirring often, 5 minutes. Add the garlic; cook, stirring occasionally, 1 minute.Advertisement
Place the onion mixture in a 6-quart slow cooker. Add the tomatoes, water, cumin, cayenne, 1/2 teaspoon of the salt, and 1/4 teaspoon of the black pepper; stir well. Cover and cook on LOW until heated through, 3 to 4 hours.
Increase the heat to HIGH. Make 8 indentations in the sauce with the back of a spoon. Crack 1 egg into each indentation. Sprinkle the eggs with the remaining 1/4 teaspoon each salt and pepper. Cover and cook on HIGH until the whites are set and the yolks are to the desired degree of doneness, about 20 minutes for slighty runny yolks. Divide the eggs and sauce among 4 plates. Sprinkle with the cheese and cilantro, and serve with the tortillas.