Season the chicken: Pat chicken breasts dry and season generously with salt and pepper on both sides.
Sear the chicken: Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Sear chicken until golden brown, about 3-4 minutes per side. Remove to a plate and set aside.
Sauté aromatics: In the same pot, add remaining 1 tablespoon olive oil. Add diced onion with a pinch of salt and cook until softened, about 4-5 minutes, scraping up browned bits.
Add peppers: Add poblano peppers and jalapeño. Cook for 3-4 minutes until softened.
Bloom spices: Add garlic and cook until fragrant, about 30 seconds. Add cumin, oregano, coriander, ancho chili powder, white pepper, and cayenne. Toast spices for 60 seconds, stirring constantly.
Build the base: Pour in chicken broth, deglazing the pot. Scrape up any spices or aromatics stuck to the bottom.
Simmer chicken: Return seared chicken breasts to the pot. Bring to a simmer, reduce heat, cover partially, and cook for about 15 minutes, until chicken registers 165°F (74°C).
Shred chicken: Remove chicken to a cutting board and shred with two forks.
Add beans and chilies: While chicken shreds, add drained white beans and diced green chilies to the pot. Simmer uncovered for 5 minutes.
Return chicken and add corn: Add shredded chicken and corn kernels back to the pot. Simmer for another 5 minutes.
Add creaminess: Reduce heat to low. Slowly stir in half-and-half (or heavy cream). If using cream cheese, add in small chunks and stir until completely melted.
Finish with lime and cilantro: Stir in lime juice and fresh cilantro. Taste and adjust salt and pepper as needed.
Rest briefly: Allow chili to rest for 5 minutes before serving.
Serve: Ladle into bowls and top with your favorite toppings like avocado, cheese, sour cream, or tortilla chips.