Cheese Grits:

1. In a large 6-quart saucepan, melt the butter over medium-high heat. Add the diced onion and sauté until softened. Stir in the minced garlic and cook for about 30 seconds until fragrant.
2. Pour in the milk, chicken broth, salt, cayenne pepper, and smoked paprika. Bring to a gentle boil. Slowly whisk in the grits, ensuring there are no clumps. Reduce the heat to medium-low. Cover and let simmer for 12–20 minutes, stirring occasionally, until thick and creamy.
3. Remove from heat and stir in the shredded cheddar cheese until fully melted. Pour in the heavy cream and stir until smooth. Taste and adjust seasoning if needed. If the grits are too thick, stir in ¼–¾ cup additional milk or water until the desired consistency is reached.

Shrimp Stock:

1. In a medium saucepan, heat 1 tablespoon butter and 1 tablespoon olive oil over medium heat. Add ¼ cup onion, ¼ cup bell pepper, and 1 tablespoon celery. Sauté until softened.
2. Toss in the reserved shrimp shells and heads, cooking for about 1 minute. Stir in 1 clove minced garlic and sauté for another 30 seconds. Pour in the white wine to deglaze the pan, scraping up any browned bits.
3. Add enough water to just cover the shrimp shells, then add the bouillon cubes. Bring to a boil, then lower to a simmer and reduce by half.

Shrimp and Andouille:

1. While the stock reduces, season the shrimp generously with Cajun seasoning and set aside. Heat a large, heavy-bottomed skillet (cast iron preferred) over high heat. Add 1 tablespoon olive oil.
2. Sauté the andouille sausage until lightly browned. Remove with a slotted spoon and set aside. Keep the skillet on high heat. Add the shrimp in a single layer and cook undisturbed for 1 minute. Flip and cook for another minute, then immediately remove from the pan and set aside.

Sauce:

1. Return the skillet to medium heat and add the remaining butter. Stir in the remaining onion, celery, and bell pepper. Sauté until softened, adding another tablespoon of olive oil if needed. Add the remaining minced garlic and all of the thyme, sautéing for about 30 seconds.
2. Remove the pan from heat, pour in the brandy, and carefully deglaze the pan. Strain the reduced shrimp stock into the skillet, discarding the solids. Whisk in the demi-glace and bring to a boil. Let simmer for 5 minutes until slightly thickened.
3. Stir in the heavy cream and reduce until the sauce coats the back of a spoon.

Finish and Serve:

1. Return the cooked shrimp, andouille sausage, and any accumulated juices to the pan. Stir well and let heat through for 1 minute. Remove from heat, taste, and adjust seasoning as needed. Stir in the fresh parsley.
2. Spoon a generous portion of cheese grits onto a plate or shallow bowl. Ladle the shrimp, sausage, and sauce over the grits. Garnish with fresh chives or scallions. Serve immediately.