Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced onion and jalapeño (if using) and cook for 4–5 minutes, stirring occasionally, until the onion is soft and translucent. Add the minced garlic and cook for 30 seconds more until fragrant.
Stir in the ground cumin, oregano, chili powder, smoked paprika, salt, and black pepper. Cook for 1 minute, stirring constantly, until the spices darken slightly and smell toasty.
Pour in the chicken broth and scrape up any browned bits from the bottom of the pot. Stir in the diced green chilies and the drained cannellini beans. Nestle the chicken breasts into the liquid — they should be mostly submerged. Bring to a gentle boil, then reduce the heat to maintain a steady simmer.
Simmer for 15–18 minutes, until the chicken is cooked through and shreds easily (165°F / 74°C internal temperature). Remove the chicken breasts to a plate or cutting board and shred them with two forks into bite-sized pieces.
Reduce the heat to low. Add the cubed cream cheese to the pot and stir gently until it melts completely into the broth, about 2–3 minutes. Stir in the shredded chicken, sour cream, lime juice, and chopped cilantro. Taste and adjust salt and pepper.
Ladle the chili into bowls while hot. Set out the toppings — shredded cheese, crushed tortilla chips, extra sour cream, sliced jalapeños, cilantro, and lime wedges — and let everyone load up their own bowl.
