Place a large Dutch oven over medium heat and add the olive oil. Once shimmering, add the diced onion and cook for 5-7 minutes until soft and translucent. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the cumin, oregano, chili powder, salt, and pepper over the onions. Stir constantly for 30-45 seconds to bloom the spices and deepen their flavor.

Pour in the chicken broth, scraping any browned bits from the bottom of the pot. Stir in the diced green chiles. Gently place the whole chicken breasts into the liquid. Bring to a simmer, then reduce heat to low, cover, and cook for 15-20 minutes, or until chicken is cooked through (165°F / 74°C).

Carefully remove the chicken to a cutting board and shred it using two forks. While shredding, add the rinsed and drained cannellini beans to the pot. Return the shredded chicken to the pot and simmer for 10 minutes to let flavors meld.

Reduce heat to the lowest setting. Stir in the heavy cream. Add the softened cream cheese in chunks, stirring gently until it has completely melted and the chili is smooth and velvety. Do not let it boil. Turn off the heat and stir in the fresh lime juice and chopped cilantro. Taste and adjust seasoning if needed before serving.