Purée one can of the white beans together with 1 cup of the chicken broth in a blender or food processor until smooth, then set this mixture aside along with the remaining whole beans.
Warm the olive oil in a large Dutch oven over medium-high heat, then add the onion, jalapeño, and poblanos.
Sauté the vegetables for about 5 minutes, stirring often, until they've softened.
Stir in the garlic and cook for another minute, then add the cumin, coriander, and ancho chile powder, stirring constantly for about a minute so the spices release their aroma.
Pour in the rest of the broth along with the puréed bean mixture and a pinch of salt, bring everything to a boil, then lower the heat and let it simmer gently, uncovered, for roughly 20 minutes.
Fold in the shredded chicken, the reserved whole beans, corn, and lime juice, then let the pot come back to a light simmer.
Cook for about 5 more minutes until everything is warmed through, then taste and add more salt or lime juice if needed, finishing with the cilantro stirred in at the end.
Ladle the chili into bowls and serve warm, topped with sour cream, crushed tortilla chips, and a lime wedge on the side (keep in mind the broth looks thin at first but thickens naturally as it sits).