Heat the oil in a medium or large stock pot over medium heat.: When the olive oil warms, you should see it shimmer and feel a slight perfume of olive when you carefully hover your hand above the pot. This stage is about creating a glossy, hot surface that will transfer heat evenly to the aromatics. If the oil smokes aggressively, the pan is too hot and will impart a bitter flavor, so lower the heat and start again. Proper temperature ensures the onion softens rather than browns too quickly, building a sweet foundation for the soup.
Add the onions and garlic and sauté until the onions are translucent.: As the onion and garlic cook, you will notice a shift from sharp raw bite to warm, sweet aromatics; the kitchen will fill with a fragrant, savory smell. Stir periodically so the pieces cook evenly and the garlic does not stick to the bottom. If the garlic starts to brown too quickly, pull the pan off the heat briefly to avoid a bitter taste. The translucent stage is the visual cue indicating that the base is ready for spices.
Add the seasonings and stir.: Adding the ground cumin , dried oregano , salt , and pepper to the warm aromatics releases their essential oils and intensifies the aroma. You should hear a faint sizzle as the spices hit the oil, and the smell will become more complex and inviting. Stir for about 30 seconds so the spices bloom, but do not let them burn. A common mistake is skipping this step, which can result in a flatter tasting broth.
Add the remaining ingredients (except for the tortilla strips and lime juice) to the top and mix to combine. Reduce the heat to a simmer, cover, and cook for 30 to 45 minutes.: When you add the pureed cannellini beans , whole beans, canned tomatoes , green chilies , creamed corn , whole kernel corn , canned black beans , and shredded rotisserie chicken , the pot will look busy and colorful. Stir gently so the pureed base disperses evenly, then lower the heat so the surface shows slow, gentle movement and small bubbles occasionally break. This long simmer melds the flavors deeply and lets the spices soften and harmonize. If the pot is boiling vigorously, reduce the heat; an aggressive boil can break down textures and cause the soup to reduce too quickly.
Serve with tri-color tortilla strips and a squeeze of lime juice.: At service, add crunchy tri color tortilla strips and a fresh squeeze of lime juice to each bowl for contrast and brightness. The aroma of the hot broth against the crisp tortilla is immediate, and the lime lifts the entire profile, making the flavors pop. Add the strips right before serving to preserve crunch. A pitfall is adding them too early, which will yield limp toppings and lose the textural delight.