Prep aromatics: Dice onion, mince jalapeños (seeded), and mince garlic. Have everything ready before cooking begins.
Sauté aromatics: Heat olive oil in Dutch oven over medium-high. Cook onion 5-6 minutes until softened. Add garlic and jalapeños, cook 1-2 minutes until fragrant.
Bloom spices: Add all spices directly to aromatics. Stir constantly 1 minute to bloom in oil and intensify flavors.
Add chicken and broth: Add whole chicken to pot. Pour in chicken broth to cover. Add green chiles. Bring to gentle boil, reduce to medium-low.
Simmer chicken: Cook 20-25 minutes until chicken is cooked through and very tender.
Shred chicken: Remove chicken with tongs. Shred with two forks into bite-sized pieces. Return to pot.
Add beans and corn: Add drained beans and corn. Mash approximately ¼ of beans in pot with potato masher for natural thickening. Simmer 5 minutes.
Make creamy mixture: Whisk softened cream cheese and sour cream until completely smooth. Add heavy cream and whisk until blended.
Add cream mixture: Reduce heat to low. Stir cream cheese mixture into chili constantly until smooth. Don't boil.
Finish: Stir in lime juice and cilantro. Taste and adjust seasoning. Simmer gently 5-8 minutes.
Serve: Ladle into bowls. Top with Monterey Jack cheese, sour cream, cilantro, jalapeños, lime wedge, and tortilla chips.