Boil 4 cups of chicken stock in a 3-quart pot, then whisk in the grits and ½ teaspoon salt and return to a boil. Let it cook over low heat for 8 minutes, whisking occasionally, until thickened. It should be stiff, not dry or runny.
Whisk in the butter, grated cheese, and spices. Cover the pot and keep it warm over low heat. Just before serving, stir in the ½ cup of cream, adding a little more if needed. Taste and adjust seasonings as desired.
Melt the bacon grease in a large skillet over medium-high heat and heat until shimmering. Saute the andouille sausage for 4 minutes, stirring occasionally, then remove it from the pan. Add the green onion and minced garlic and cook until fragrant, roughly 2 minutes.
Deglaze the pan by pouring in the white wine and stirring for a minute.
Add the shrimp (make sure they have been peeled and deveined) sprinkle on the spices and add the lemon juice. Cook for 3 minutes while constantly stirring. Turn the heat down to a simmer, sprinkle in the flour on top, and stir it in. Add the cream and stir the sauce until it is the right consistency. Cook the sauce for 2-3 minutes to remove the flour taste.
Add the browned sausage to the sauce and stir until heated through.
Divide the grits among six shallow bowls or plates. Place 5 or 6 large shrimp on each plate, then divide the sausage and sauce evenly among the bowls. Garnish with a sprinkle of fresh thyme and serve immediately.