Preheat the oven to 425°.
Roast the poblanos over your gas stovetop until charred. Place in a plastic bag and let steam 10 minutes. With your hands, remove most of the charred skin. Remove tops and seeds and chop the peppers. Do this step the day before to avoid extra time when making this dish. It takes about 10 minutes for the chiles to char.
In a large cast-iron skillet, heat the olive oil. Add the chopped roasted poblanos, tomato halves and cook over moderate heat 4 minutes. Stir in the garlic, cook 1 more minute. Add the tomato sauce, chili powder and oregano and cook over low heat until thickened, 10 minutes.
Taste the sauce and add a splash of vinegar.
Crack the eggs into the tomato sauce and top with the cheese. I like to sprinkle the cheese around the eggs, so I can see if they're over cooking. Bake until set, about 10 minutes. Watch the eggs closely to get them to your desired doneness. 10 minutes will more than likely cook them to the hard stage. Garnish with cilantro and jalapeños and serve with corn chips.
While the eggs are in the oven, chop the cilantro and slice the jalapenos. Serve immediately with garnishes.