Char the vegetables black, fry the puree until the oil separates, and whatever chicken is left in the fridge becomes the best soup of the week.
Tear the anchos into a blender with 2 cups of the broth. Let them soften about 15 minutes.
Cut the top off the head of garlic, drizzle with olive oil, wrap it in foil, and roast at 400°F for 35–45 minutes until the cloves are soft enough to squeeze out. Start this first — it's the longest thing in the recipe, and everything else happens while it's in the oven.
Dry skillet, high heat, no oil. Onion cut-side down, jalapeños alongside. Take them well past brown to actual black in spots — that char is the smoke in this soup.
Pull the vegetables out and pour the whole can of diced tomatoes straight into the hot skillet. Scrape everything stuck to the bottom up into the tomatoes.
Into the blender with the soaking anchos goes the charred onion and jalapeños, the roasted garlic (oil and all), the tomatoes from the pan, the chipotles and adobo, the crushed tortilla chips, cumin, and oregano. Blend a full minute — you want it completely smooth, not almost smooth.
Heat the peanut oil in a pot until it shimmers, then pour in the puree — stand back, it spatters. Fry about 8 minutes, stirring. It's done when it darkens to a deep brick color, holds a trail behind the spoon, and the oil starts breaking out around the edges. This step is the whole recipe. Don't shortcut it.
Add the remaining 4 cups of broth and the salt. Simmer uncovered about 20 minutes.
Stir in the frozen corn, drained black beans, and diced chicken. Heat 3–4 minutes and no longer — the chicken is already cooked, and boiling it again just dries it out. Off the heat, squeeze in both limes, then taste and adjust salt.
Chips in the bottom of the bowl first, soup ladled over them, toppings last. The chips underneath go soft and thicken the soup; the ones on top stay crunchy. You want both.
Toppings go on last — chips underneath, chips on top.
