Cook onion and poblano: Heat oil in a Dutch oven over medium-high. Add onion, poblano, and salt; sauté until onion softens, about 3 minutes.
Add garlic and spices: Add garlic to pan; sauté 3 minutes. Stir in cumin, oregano, and smoked paprika; cook until fragrant, 30 seconds to 1 minute, stirring constantly.
Add stock, salsa, and beans: Stir in chicken stock, salsa verde, and beans; bring to a boil. Reduce heat to medium-low and cook for 10 minutes.
Warm cream cheese: Meanwhile, place cream cheese in a medium microwave-safe bowl. Microwave on 50% power for 1 minute or until very soft.
Combine cream cheese and chili: Ladle about 1 cup hot broth mixture into bowl with cream cheese; stir until smooth.
Add cream cheese and chicken and heat through: Stir cream cheese mixture into chili, then gently stir in chicken. Cook until thoroughly heated, about 2 minutes. Ladle chili into bowls and top with preferred garnishes.
