Bake the Tortillas: Preheat your oven to 450°F. Arrange the corn tortillas in a single layer on a baking sheet. Lightly brush them with oil and sprinkle a pinch of kosher salt on top. Bake for 15 to 20 minutes, or until the tortillas are crisp and golden.
Roast the Vegetables for the Salsa: Cut the onion into ¼-inch-thick slices. Spread the onion slices, tomatillos, garlic clove, jalapeño, and poblano chile on a large baking sheet. Roast in the oven without oil until the vegetables are charred and softened, about 15 to 20 minutes. It's fine if the onions and garlic develop some color but don't fully soften.
Blend the Salsa: Place the roasted vegetables in a food processor along with 1 cup of chopped cilantro, lime juice, and ½ teaspoon of salt. Process the mixture until smooth, yielding approximately 2 cups of salsa. Taste the salsa and adjust seasoning with additional lime juice or salt as needed.
Prepare the Baking Dish: Lower the oven temperature to 375°F. Spoon a small amount of the salsa to coat the bottom of a 9-inch square baking dish or a 1½- to 2-quart shallow gratin dish.
Assemble the Chilaquiles Layers: Lay some of the crisp tortillas on top of the salsa in the dish, then add more salsa and a handful of grated Monterey Jack cheese. Continue layering tortillas, salsa, and cheese until all the ingredients are used up, finishing with a layer of salsa and a sprinkle of cheese. Set aside ½ cup of the cheese for garnish. Transfer the dish to the oven and bake for 20 minutes.
Add the Eggs: Crack the eggs over the top of the chilaquiles, spacing them evenly. Lightly season the eggs with salt and freshly ground black pepper. Return the dish to the oven and bake for another 6 to 10 minutes, or until the egg whites are set but the yolks remain soft and runny.
Prepare the Garnish: While the eggs bake, dice the remaining onion into small pieces to make ¼ cup. Mix it with the remaining ½ cup of cilantro in a small bowl.
Finish and Serve: Once the eggs are cooked to your liking, remove the dish from the oven. Sprinkle the onion-cilantro mixture on top and garnish with the reserved cheese, toasted pepitas, and a dollop of sour cream or crema, if desired. Serve immediately and enjoy your chilaquiles!