Heat a large pot over medium heat. Add the sliced andouille and cook until browned and fragrant, stirring occasionally so it doesn’t stick.

Push the sausage to the side and add the chopped onions, carrots, and celery. Sauté until the vegetables soften and the onion becomes translucent, about 5–7 minutes.

Add the diced potatoes and sprinkle in the Cajun spices. Stir to coat the potatoes and toast the spices for 30–60 seconds.

Pour in enough water or broth to just cover the ingredients. Increase heat to bring the pot to a boil.

Once boiling, reduce heat to low and simmer until the potatoes are tender when pierced with a fork, about 15–20 minutes depending on dice size.

Stir in the heavy cream, then add the shredded cheddar a little at a time, stirring until everything is smooth and melted.

Taste and adjust seasoning with salt and more Cajun spice if needed. Serve warm right away.