Heat the olive oil in a large skillet over medium heat. Add the chopped onion and sauté until the pieces become translucent. Add the tomatoes along with their juices. If using whole canned tomatoes, break them apart with a spatula. If using fresh tomatoes, allow extra time for them to soften, as they require a longer cooking period.

Stir in the diced green chiles and any optional seasonings, such as chipotle chili powder, adobo sauce, chili powder, or cumin. Bring the mixture to a gentle simmer, reduce the heat to low, and allow it to cook for approximately 10 minutes, stirring occasionally. Season with salt to taste. Reduce the heat to warm while the remaining components are prepared.

Preheat the oven to 150°F (65°C). Place the serving plates inside to keep them warm. Do not use plastic plates.

In a large nonstick skillet, heat approximately 1 teaspoon of olive oil over medium-high heat. Warm each tortilla for 1–2 minutes per side or until softened and lightly blistered. Transfer the tortillas to the warmed plates and keep them in the oven while preparing the eggs.

Using the same skillet, add approximately 2 teaspoons of butter. Heat over medium-high. Crack the eggs into the skillet and cook for 3–4 minutes for runny yolks or slightly longer for firmer yolks.

Spoon a small amount of the prepared salsa onto a warmed plate. Place one tortilla over the salsa, top with a fried egg, and add additional salsa over the top. Garnish with fresh cilantro if desired. Serve one or two eggs and tortillas per plate.