• Peel the white onion and cut in half. Finely chop half; very thinly slice half for garnish.
• Finely chop, press, or grate enough garlic to measure ½ teaspoon.
• If using the serrano, remove the stem, ribs, and seeds; finely chop the serrano. Wash your hands after handling.

In a large frying pan over medium heat, warm 1 tablespoon oil until hot but not smoking. Add the chopped onion, season with salt and pepper, and cook, stirring occasionally, until starting to soften, 3 to 5 minutes. Stir in the garlic, chili powder, and as much serrano as you like and cook until fragrant, about 1 minute.
Add the tomatillos and vegetable broth. Bring to a boil, reduce to a simmer, and cook, stirring occasionally, until the sauce thickens, 5 to 6 minutes.
While the salsa verde simmers, prepare the remaining ingredients and cook the eggs.

• Rinse the beans.
• Coarsely chop the cilantro; divide into two equal portions, one for stirring into the chilaquiles and one for garnish.
• Cut the avocado in half lengthwise. Remove the pit, scoop out the flesh, and cut the flesh into ¼-inch-thick slices.

• Crack the eggs into a medium bowl and season with salt and pepper. Using a whisk or fork, lightly beat until just blended.

In a small frying pan over medium heat, warm 1 tablespoon butter or oil until hot but not smoking. Add the eggs and cook, stirring gently, until just set but still moist, 2 to 3 minutes.

To the pan with the salsa verde, stir in the beans and cook until heated through, 1 to 2 minutes. Remove from the heat and season to taste with salt and pepper. Stir in the tortilla chips, scrambled eggs, and half the cilantro.

Transfer the chilaquiles to individual bowls. Garnish with the yogurt, avocado, a few onion slices, and the remaining cilantro. Crumble the queso fresco over the top and serve.