Preheat the broiler to high and use aluminum foil to line a sheet pan.
Arrange the vegetables over the sheet pan and broil until blackened in places and tender.
Put the vegetables in a blender and puree with the oregano, cilantro and chile powder, adding some water if needed.
Drizzle the oil into the puree mixture and mix a little more.
Heat 2 cups of oil in a skillet (cast iron if you have it).
Stack the tortillas and then cut into squares.
Fry the tortilla pieces in the oil until browned, then drain on paper towels.
Discard most of the used oil from the pan, leaving about a tablespoon of oil in there.
Put the green chile mixture in there and cook for a few minutes.
Put the tortilla chips back in there and toss to coat.
Fry the eggs in another pan and serve with the chilaquiles.
Garnish with Mexican crema and cheese, and add radish and cilantro too if liked.
Serve immediately.