Slice the Andouille sausage into 1/4-inch pieces and heat a large skillet over medium heat. Add the sausage slices and cook for 4-5 minutes, stirring occasionally, until browned and crispy. Once cooked, remove the sausage from the skillet and set aside, leaving any rendered fat for the next steps.

In the same skillet, lower the heat and add 1 tablespoon of butter to the residual sausage fat. Once melted, toss in the finely chopped shallot and minced garlic, sautéing for about 2 minutes until they become translucent and fragrant.

Sprinkle the 1 tablespoon of flour into the skillet, stirring continuously to combine with the shallots and garlic. Cook for about 1 minute, allowing the flour to slightly brown and form a roux.

Slowly whisk in 3/4 cup of chicken broth and 2/3 cup of heavy cream, ensuring there are no lumps. Increase the heat slightly and let the mixture simmer for 3-4 minutes, stirring frequently, until it thickens slightly.

Stir in the 2 tablespoons of grated Parmesan cheese, chopped sun-dried tomatoes, 1/4 teaspoon of dried thyme, and 1/4 teaspoon of red pepper flakes. Cook for an additional 1-2 minutes, mixing until the cheese is melted.

Add the cooked pasta to the skillet, tossing gently to coat every piece in the luscious sun-dried tomato sauce.