Preheat oven to 400°F (200°C). Place whole poblano peppers on a baking sheet. Roast for 20-25 minutes, turning once, until skin is blistered and slightly charred. Transfer peppers to a bowl, cover tightly with plastic wrap, and let steam for 10 minutes. Once cool enough to handle, peel, core, and seed the poblanos. Dice them finely.

While poblanos roast, season chicken breasts with 1/2 tsp salt and 1/4 tsp black pepper. Heat 1 tbsp olive oil in a large Dutch oven or stockpot over medium-high heat. Add chicken and sear for 3-4 minutes per side until lightly browned. Remove chicken from pot and set aside on a plate; it doesn't need to be cooked through.

Reduce heat to medium. Add another 1 tbsp olive oil to the pot if needed. Add chopped yellow onion and cook, stirring occasionally, until softened, about 5-7 minutes. Add minced garlic and cook for 1 minute more until fragrant.

Stir in diced roasted poblano peppers, canned diced green chiles (undrained), ground cumin, dried oregano, white chili powder, smoked paprika, and cayenne pepper (if using). Cook for 1-2 minutes, stirring constantly, until fragrant.

Pour in chicken broth and stir well, scraping up any browned bits from the bottom of the pot. Add rinsed and drained cannellini beans. Bring the mixture to a simmer.

Carefully return the seared chicken breasts to the simmering chili. Cover the pot and reduce heat to low. Simmer for 15-20 minutes, or until chicken is cooked through and easily shredded. Remove chicken from the pot and shred it using two forks. Return shredded chicken to the pot.

Add the cubed cream cheese and heavy cream (or half-and-half) to the chili. Stir gently until the cream cheese is fully melted and incorporated, creating a creamy texture. Taste and adjust seasoning with additional salt and black pepper as needed.

Ladle the hot white chicken chili into bowls. Garnish with chopped fresh cilantro, diced avocado, a dollop of sour cream or Greek yogurt, a squeeze of fresh lime, and crushed tortilla chips, if desired.