Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion, celery, and carrots. Cook, stirring occasionally, until the vegetables have softened, which should take about 5-7 minutes. This step is crucial for building a flavorful base for your chili.

Stir in the minced garlic, cumin, chili powder, and cayenne pepper (if using). Cook for another minute until fragrant. Add the cooked, shredded chicken and stir to combine.

Add the cannellini beans, great northern beans, and chicken broth to the pot. Bring the mixture to a simmer, then reduce the heat to low, cover, and let it cook for 15-20 minutes to allow the flavors to meld.

Stir in the heavy cream and diced green chilies. Continue to simmer for another 5-10 minutes, or until the chili is heated through and slightly thickened.

Season the chili generously with salt and black pepper to taste. Ladle into bowls and garnish with fresh cilantro and shredded Monterey Jack cheese, if desired.