1. Heat olive oil in a large Dutch oven over medium-high heat. Add cubed chicken and sliced andouille in a single layer. Cook, stirring occasionally, 5–7 minutes until chicken browns on the outside and sausage develops caramelized edges. The sausage renders its flavored fat into the pot — this builds the flavor foundation of the entire chili.

2. Add diced onion, celery, bell pepper, and jalapeño to the pot. Cook over medium heat, stirring frequently, about 5 minutes until the vegetables soften and turn translucent. The Cajun trinity releases a deeply savory aroma at this stage — this is the flavor backbone of the dish taking shape.

3. Add minced garlic, cumin, smoked paprika, chili powder, and cayenne. Stir constantly for 60–90 seconds until the spices bloom in the hot fat and smell intensely fragrant. Sprinkle flour over everything and stir 1–2 minutes until the raw starch taste cooks out completely.

4. Pour in chicken broth gradually while stirring constantly to dissolve the flour without lumps. Add drained and rinsed white beans and stir to combine. Bring to a simmer over medium-high heat, then reduce to medium-low and simmer uncovered for 10 minutes to let flavors meld and the broth thicken slightly.

5. Add shrimp and cook exactly 2–3 minutes until they turn pink and opaque throughout. Remove the pot from the heat immediately — shrimp overcooked by even 60 extra seconds turn rubbery. Stir in heavy cream off the heat to prevent curdling. Taste and adjust salt, pepper, and cayenne before serving.

6. Ladle chili into deep bowls. Top each serving with sliced green onions, a dollop of sour cream, shredded cheese, and sliced jalapeño. Serve with lime wedges and cornbread or crusty French bread for dipping.