Crisp the bacon: In a large pot or Dutch oven over medium heat, cook the chopped bacon until crispy, 6–8 minutes.
Remove with a slotted spoon and set aside, leaving about 1 tablespoon of bacon fat in the pot.
Sauté aromatics: Add the onion and green bell pepper to the pot. Cook until softened, 4–5 minutes. Stir in garlic and cook 30 seconds, until fragrant.
Bloom the spices: Add cumin, chili powder, smoked paprika, onion powder, garlic powder, oregano, salt, and pepper.
Stir for 30 seconds to toast the spices.
Add chicken and broth: Place the chicken breasts into the pot. Pour in the chicken broth and add the diced green chiles. Bring to a gentle boil, then reduce to a simmer.
Cover and cook 18–22 minutes, until the chicken is cooked through.
Shred the chicken: Remove the chicken to a cutting board and shred with two forks. Return the shredded chicken and any juices to the pot.
Make it creamy: Stir in the cream cheese cubes until melted and smooth. Reduce heat to low, then add heavy cream and cheddar cheese.
Stir until the cheese is fully melted and the chili is creamy.
Finish with bacon and taste: Stir the crispy bacon back in, reserving a little for topping. Taste and adjust salt, pepper, or chili powder as needed. For more kick, add jalapeño slices now.
Thicken or loosen: Simmer uncovered for 5–10 minutes to thicken, or add a splash of broth if you prefer it looser.
Serve: Ladle into bowls and top with extra cheddar, green onions, cilantro, and a squeeze of lime if you like.