Prepare your ingredients: dice the Yukon Gold or red potatoes into bite-sized pieces and chop the onion, bell peppers, and celery. Mince the garlic and slice the andouille sausage.

In a large pot, combine a tablespoon of butter and a tablespoon of olive oil over medium heat. Add the sliced andouille sausage. Cook for 5-7 minutes until browned and fragrant, then remove from pot.

In the same pot, add the chopped onion, celery, and bell peppers. Cook until softened and translucent, about 5 minutes. Then add the minced garlic and sauté for another minute.

Return the cooked sausage to the pot, then add diced potatoes, Cajun seasoning, and enough chicken broth to cover the ingredients. Bring to a gentle boil and then reduce heat to a simmer, covering for 15-20 minutes.

Once the potatoes are tender, use an immersion blender to puree a portion of the soup, blending until smooth while leaving some chunks for texture.

Gradually stir in about 1 cup of heavy cream or half-and-half over low heat. Warm gently without boiling and taste to adjust seasoning.

Ladle the soup into bowls, garnishing with green onions, shredded cheese, or bacon bits as desired. Serve alongside crusty bread or cornbread.