Soften the cream cheese. Let the cream cheese sit at room temperature near the pot while you prepare the chili.
Sauté the onion. Heat 1 tablespoon of olive oil in a large pot over medium heat. Add the diced onion and cook for about 5-6 minutes, until softened.
Bloom the spices. Add 2 more tablespoons of olive oil, cumin, oregano, garlic powder, chili powder, and cayenne. Stir and cook in the oil for 3–4 minutes over medium to low heat, stirring frequently so the spices become fragrant without burning. This step builds deeper flavor throughout the chili.
Add the green chiles and broth. Stir in the diced green chiles, then pour in 4–5 cups of chicken broth. Bring to a gentle simmer and cook for a few minutes.
Add beans & blend. Add drained pinto beans. Use an immersion blender to blend a portion of the soup until it reaches your preferred consistency. Alternatively, carefully transfer some of the broth to a blender, blend, and return it to the pot.
Add the chicken. Stir in the shredded chicken and simmer until heated through.
Prepare the cream cheese. Dice the softened cream cheese. Remove about 1 cup of warm broth from the pot and whisk it with the cream cheese in a separate bowl until smooth and mostly lump-free.
Finish the chili. Pour the cream cheese mixture back into the pot and stir well. Cook gently for a few more minutes, stirring until the chili is creamy and evenly combined. Avoid boiling vigorously.
Season and serve. Taste and adjust the salt, pepper, and cayenne as needed. Ladle into bowls over rice and serve with your favorite toppings.