Fry the tortillas strips in oil until golden brown. Drain on paper towels. Set aside.: The sizzling sound will tell you they are crisping up and the oil will shimmer when ready, producing ribbons of golden brown that provide a toasty, slightly nutty note against the silky chili. Watch closely and flip so each strip browns evenly, removing them when they reach a light golden color to avoid bitterness. After frying, drain on paper towels to remove excess oil, which otherwise makes them soggy. A common mistake is overcrowding the pan, which drops the oil temperature and prevents proper crisping, so fry in batches if needed.
Heat the olive oil in a large skillet (or Dutch oven) over medium-high heat.: You will notice a faint aroma as the oil warms, and the surface should ripple gently when it is ready. This step primes the cooking surface so aromatics cook evenly rather than sticking. If the oil smokes, lower the heat to prevent burnt flavors. Using a heavy bottom pot helps distribute heat and avoids hot spots.
Add the onion and sauté for about 5 minutes, until softened. Add the garlic, and cook for 1 to 2 minutes longer.: The onion will go from opaque to translucent and begin releasing a sweet aroma, signaling it has mellowed and will no longer taste sharp. Stir occasionally so each piece softens evenly and develops a touch of color without burning. If you rush this stage by increasing the heat, you risk charring the edges, which introduces bitter notes, so be patient and listen for gentle sizzling.
Add the tomatoes, tomatillos, and jalapeño. Cook until the tomatillos are tender, stirring occasionally, about 10 to 12 minutes.: The garlic will release a fragrant, savory scent when it hits the warm oil, an important layer for the final depth of the dish. Cook briefly until the raw edge is gone and the aroma becomes nutty, but remove from heat or add the next items quickly, because garlic can brown and turn bitter in a flash. If you smell any scorch, stop and lower the heat immediately.
Add the chicken stock, green chiles, chicken, oregano, cumin, cilantro, beans, and lime juice.: As these hit the pot the mixture will begin to steam and the tomatillos will soften, releasing tangy juices that marry with the tomatoes. Stir to combine and scrape any browned bits from the bottom for extra flavor. Keep the heat moderate so the tomatillos can tenderize and their tartness can mellow, otherwise they may remain tough or taste astringent.
Simmer for about 10 minutes, season with a healthy pinch of salt and pepper. Taste and adjust seasonings, if necessary.: You'll see the tomatillos collapse slightly and the mixture will thicken, with bright green and red pieces melding together. This breakdown is crucial because it integrates their acidity into the broth, rather than leaving sharp, raw pockets. Stir every few minutes to prevent sticking, and if the pot starts to dry, add a splash of stock to maintain moisture. Overcooking can lead to a flat, muted flavor, so watch for that tender but still vibrant stage.
Ladle the chili into serving bowls. Serve garnished with a dollop of sour cream, shredded cheese, and fried tortilla strips.: When these go in the pot the aroma shifts toward a balanced stew, with savory, herbal, and acidic elements blending. The stock sets the consistency, the chiles and spices add depth, and the beans and chicken bring body. Stir gently to incorporate everything and bring the mixture to a gentle simmer. A common error is adding salt too early, so hold off seasoning until after simmering to better judge the final balance.
Simmer for about 10 minutes, season with a healthy pinch of salt and pepper: During simmering the flavors marry and the liquid reduces slightly, concentrating taste while the beans soften into the broth. Taste and adjust salt and pepper, and if the pot feels flat, a touch more lime juice can open it up. Do not let it boil vigorously, as that can break down the chicken and beans excessively and turn the texture pasty.
Taste and adjust seasonings, if necessary: After the simmer the aroma and flavor will be most telling, so sample for salt, acidity, and heat. If it needs brightness, add more lime juice ; if it needs warmth, a pinch more ground cumin helps. Adjust incrementally, tasting between additions, because big jumps in seasoning can be hard to dial back.
Ladle the chili into serving bowls: As you portion the chili, you will notice the stew has a silky body with pockets of shredded chicken and beans. Garnish each bowl with a dollop of sour cream , a sprinkle of shredded cheddar cheese and Monterrey Jack cheese , and a handful of the fried flour tortilla strips to add coolness, salt, and crunch. Serve immediately, because the tortilla strips will soften over time and lose their contrast.