To make the grits, bring the chicken broth to a boil in a heavy-bottomed stockpot or large saucepan. Slowly pour in grits, stirring constantly. Reduce the heat to low and continue to stir so that the grits so not settle to the bottom and scorch. In about 5 minutes, the grits will plump up and become a thick mass.
Continue to cook the grits for about 20 to 25 minutes, stirring frequently. The grits should have absorbed all of the stock and become soft.
Stir in the heavy cream and cook for another 10 minutes, stirring frequently. The grits should have a thick consistency and be creamy, like oatmeal. Season, to taste, with salt and white pepper. Keep warm over low heat until ready to serve. If the grits become to thick, add warm chicken broth or water to thin them down. To make the Shrimp and Sausage: Preheat the oven to 400 degrees F. Place the Italian sausage on a baking sheet with raised sides. Place on the top rack of the oven and bake for 10 to 15 minutes or until the sausage is firm and the juices run clear. Cool and cut into small bite size pieces.
Heat the olive oil in a heavy bottomed frying pan over medium heat. Add the sausage and saute for 2 minutes to brown slightly. Add the shrimp and saute until they begin to turn pink, no longer than 1 minute.
Add 1 cup of chicken broth to deglaze the pan. Add the Tasso Gravy and 1 tablespoon of the parsley. Bring up to a boil and simmer for 1 minute. The last 1/2 cup of the chicken stock is to be used to thin the gravy, if needed.
Divide the hot grits between 8 warm bowls. Spoon the shrimp, sausage mixture over the grits. Sprinkle with the remaining tablespoon of parsley and serve immediately.
Melt the butter in a heavy bottomed saucepan over low heat. Add the tasso. Saute for 1 minute, browning slightly. Make a roux by adding the flour and stirring until well combined.
Continue to cook over low heat for 5 minutes. Stirring frequently until the roux develops a nutty aroma. Turn the heat up to medium and gradually add 2 cups of the chicken broth, stirring vigorously. Keep stirring constantly until the broth begins to thicken and is smooth. Gradually add the remaining 2 cups of broth, stirring constantly until the broth thickens into gravy. Reduce the heat and simmer over low heat for 15 minutes to cook out the starchy flavor. Add the parsley. Simmer for another 5 minutes. Season, to taste, with salt and white pepper.
If using large shrimp, allow 6 per person; for medium sized shrimp, 8 to 10 shrimp.