Place the potato chunks in a large microwave-safe bowl with 2 to 3 tablespoons of water. Cover loosely and microwave on high, stirring occasionally, until the potatoes are nearly tender, about 5 to 8 minutes. Set aside.

In a large stock pot, heat the butter and olive oil over medium heat. Add the onion, celery, and bell pepper, and sauté for 4 to 5 minutes or until the onion becomes translucent. Stir in the garlic and cook for 1 minute.

Add the sliced andouille sausage and cook for 4 to 5 minutes, stirring occasionally, until browned slightly.

Pour in the chicken or vegetable broth and bring the mixture to a simmer. Add the pre-cooked potatoes and cook for an additional 12 to 15 minutes or until the potatoes are fully tender.

Reduce the heat to low. Stir in the heavy cream and season the soup with Cajun seasoning to taste. Allow the soup to heat through, but avoid boiling.

Ladle the soup into bowls and garnish with shredded cheddar cheese and sliced green onions. Serve immediately.