Dice the Yukon Gold or red potatoes into bite-sized pieces, and chop the onions, bell peppers, and celery. Mince the garlic and slice the andouille sausage into thin rounds.

In a large pot, heat butter and olive oil over medium heat. Once melted, add the sliced sausage and sauté for about 5-7 minutes until browned.

In the same pot, add chopped onions, celery, and bell peppers. Cook for 5-6 minutes until softened. Stir in minced garlic and cook for an additional minute.

Return the sausage to the pot, sprinkle in Cajun seasoning, add the diced potatoes, and pour in the chicken broth. Bring to a boil, then reduce heat and simmer for 15-20 minutes.

Using an immersion blender, puree a portion of the soup to your desired consistency while leaving some potato chunks.

Gently stir in heavy cream, warming it through without boiling. Adjust seasoning if necessary.

Ladle the soup into bowls and garnish with sliced green onions, cheese, or crumbled bacon if desired.