Line a large baking sheet with a few layers of dry paper towels and set it aside. To a large, heavy skillet over medium heat, add 1 cup oil; when the oil is hot, working in batches, fry the tortillas until crisp and golden, 3–4 minutes per batch. Using a slotted metal spoon or spider skimmer, transfer the chips to the lined baking sheet as you continue frying the rest. Discard the oil, wipe out the skillet, and set aside.
To a medium pot, add the tomatoes, jalapeños, and garlic. Measure ¼ cup of the onions for garnish and set them aside; add half of the remaining onions to the pot, as well as enough cold water to just cover the vegetables. Bring to a boil over medium-high heat, lower the heat to maintain a strong simmer, and cook until the tomatoes are very soft, 18–20 minutes. Add ¼ cup of the cilantro and continue cooking 1 minute more. Drain the vegetables, discarding the cooking liquid. Peel and core the tomatoes and stem the jalapeños (for a milder sauce, remove and discard the japaleño seeds). Transfer the vegetables to a blender and purée to make a smooth sauce, then set aside.
In the reserved skillet, heat the remaining oil over medium heat. When the oil is hot, add all but the reserved ¼ cup of onions and cook, stirring frequently, until they are softened and translucent, 7–9 minutes. Stir in the reserved vegetable sauce and chicken bouillon powder (if using), turn the heat to medium-high, and bring to a boil. Add the fried tortillas and chicken (if using), stirring and turning to coat with the sauce. Simmer until the tortillas are tender but still chewy, 2–3 minutes. Transfer the chilaquiles to a warm platter, top with crema or sour cream, cotija cheese, and pickled jalapeños (if using), then garnish with the remaining cilantro and onions. Serve hot.