Poach the chicken: Season the chicken with 1/2 teaspoon kosher salt and a little black pepper. Place in a medium saucepan with 4 cups low-sodium chicken broth, 1 bay leaf, and a smashed clove of garlic. Bring to a gentle simmer over medium heat, reduce to low, and poach until the internal temperature reaches 165°F (about 12–16 minutes for breasts, 18–22 minutes for thighs). Remove the chicken, cover and rest 5 minutes, then shred with two forks. Reserve the poaching liquid.

Sauté aromatics and toast spices: In a 5–6 quart Dutch oven, heat 1 tablespoon neutral oil over medium heat. Add the diced onion and a pinch of salt; cook until translucent, about 6–7 minutes. Stir in the minced garlic and minced jalapeño and cook 30 seconds more. Add 1 tablespoon ground cumin and 3/4 teaspoon dried oregano and toast for 30–45 seconds until fragrant.

Add beans and simmer: Pour in 2 cups of the reserved poaching liquid (or additional chicken broth) and add both cans of drained white beans. Remove about 1 cup of beans and puree them in a blender or use an immersion blender to pulse until smooth; return the pureed beans to the pot to thicken the base. Stir in the shredded chicken, 1/2 teaspoon kosher salt, and 1/2 teaspoon black pepper.

Finish with lime and thicken: Add 1 teaspoon lime zest and 2 tablespoons lime juice, reduce heat, and simmer gently for 10–12 minutes to let flavors meld—avoid a rolling boil. Whisk 2 tablespoons cornstarch with 3 tablespoons cold water to form a slurry. Temper the slurry by whisking it into 1/2 cup hot broth taken from the pot off the direct flame, then stir the tempered mixture back into the chili and bring to a slow bubble for 1–2 minutes until slightly thickened.

Optional finishing and serve: If desired, remove from heat and stir in 1/4 cup shredded Monterey Jack or white cheddar off heat for a touch of richness. Taste and adjust salt and lime juice. Serve garnished with chopped cilantro, sliced green onions, diced avocado, and lime wedges.