For the sauce:
Roast the tomatillos: Heat a skillet or griddle over medium-high heat. Place the tomatillos, jalapeños, onion, and garlic in the pan. Dry roast them, turning occasionally, until the tomatillos are soft and slightly charred (about 7-10 minutes). The jalapeños should be slightly blistered as well. Remove from heat and let cool.

1. Blend the sauce: Once the vegetables are cool enough to handle, transfer them to a blender. Add the cilantro and a pinch of salt, and blend until smooth. Taste and adjust seasoning, adding more salt if necessary.
2. For the chilaquiles:
   Fry the tortilla chips: Heat the olive oil in a large skillet over medium heat. Once hot, add the tortilla strips or triangles and fry them for 2-3 minutes, stirring occasionally, until they are crispy and golden. Remove from the pan and drain on paper towels to remove excess oil.
3. Combine the chips and sauce: In the same skillet, pour in the green sauce and bring it to a simmer over medium heat. Add the fried tortilla chips to the pan, stirring gently to coat them in the sauce. Let them cook for 3-4 minutes until the chips soften slightly, but remain crispy around the edges.
4. Cook the eggs: While the chips are cooking in the sauce, cook your eggs. You can either fry or scramble them, depending on your preference. If you prefer poached eggs, those are also a great topping for chilaquiles!
5. Assemble the dish: Divide the chilaquiles into serving plates. Top with cooked eggs, crumbled queso fresco or shredded cheese, a dollop of sour cream, and fresh cilantro. Optionally, garnish with sliced avocado, red onion, or a squeeze of lime for added flavor.
6. Serve: Serve your Chilaquiles Verdes immediately while the chips are still crispy and the eggs are warm. Enjoy!