Heat a tablespoon of oil in a large saucepan over medium heat. Once shimmering, add the sliced Andouille sausage and cook for about 5-7 minutes, stirring occasionally, until browned and fragrant. The sausage should be nicely caramelized. Remove it from the pan and set it aside in a bowl.

In the same saucepan, season the boneless chicken with 1 teaspoon of Cajun seasoning. Increase the heat slightly and cook the chicken for around 5-7 minutes, turning occasionally, until it is golden brown on the outside and no longer pink in the center. Remove the chicken from the pot and let it rest while you prepare the vegetables.

Add 1 tablespoon of butter to the remaining drippings in the saucepan and melt it over medium heat. Toss in diced onion, celery, bell pepper, and jalapeno. Sauté for 7-10 minutes, stirring frequently, until the vegetables are tender and the onion is translucent.

Once the vegetables are softened, add the chopped garlic, ground cumin, and the remaining Cajun seasoning to the pot. Stir for about 1 minute until the aroma fills your kitchen and the spices become fragrant.

Pour in 4 cups of chicken broth, followed by the white beans and salsa verde. Add the sautéed sausage and the chicken you set aside earlier. Stir everything together and bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to low, allowing it to simmer gently for about 15 minutes.

After simmering, remove the cooked chicken from the chili and shred or slice it into bite-sized pieces. Return the shredded chicken back into the pot, mixing it gently with the rest of the ingredients.

Stir in 1/2 cup of sour cream and 1/4 cup of grated Parmesan cheese until melted and fully combined. Finish with an optional splash of lime juice, chopped cilantro, and sliced green onions for brightness. Taste and season with salt and pepper to your liking. Your hearty bowl of Cajun White Chicken Chili is now ready to be served!