In a large pot over medium heat, melt 2 tablespoons of butter. Add the diced onion and cook for 3–4 minutes, or until softened.
Add 1 teaspoon garlic and cook for 1 more minute.
Stir in the uncooked rice and 2 tablespoons of Cajun seasoning. Make sure the rice is evenly coated with the seasoning.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, reduce heat to low, cover the pot with a lid, and simmer for 20-25 minutes, undisturbed, or until the rice is tender and the liquid has been absorbed. If the liquid has not been absorbed after 25 minutes, cook for 3-4 more minutes, keeping the pot covered.
While the rice cooks, heat olive oil in a large skillet over medium-high heat. Once the oil is shimmering, add the sliced andouille and cook for 3–4 minutes per side, or until browned and crisp. Transfer sausage to a plate.
Using the same skillet as you cooked the sausage, reduce heat to medium. Add the remaining butter. Once melted, stir in the remaining garlic and Cajun seasoning and cook for 1 minute. Pour in the heavy cream and stir to combine. Simmer, scraping up any browned bits, for 3–5 minutes until slightly thickened and heated through.
To the pot of cooked rice, add the cream sauce and sausage. Stir to combine.
Garnish with chopped parsley. Serve immediately.