Heat a large pot to medium and add the andouille. Saute for 3 minutes, stirring, until lightly browned. Remove and set aside.
Make a Roux. Add vegetable oil and flour. Stir to form a paste, then cook, stirring constantly for 10-15 minutes, until the roux darkens to a rich brown.
Add the onion, jalapeno (or bell pepper) and celery. Stir and cook for 5 minutes.
Stir in the garlic and cook for 1 minute.
Stir in the tomato paste, diced tomatoes and Cajun seasonings, salt and pepper. Cook for 1 minute to let the flavors develop.
Stir in the stock and fresh thyme. Reduce heat to low and simmer for 30 minutes to thicken the gravy.
Stir in the sausage and simmer another 30 minutes or longer to your desired flavor. Adjust for seasonings.
Remove from heat and stir in the shrimp. Cover and let the shrimp cook 3-5 minutes to cook through.
While the shrimp gravy is simmering, add the butter, water (and milk or cream, if using) and optional salt to a pot. Bring to a boil.
Stir in the grits and bring back to a boil. Lower the heat, then cover and simmer 30 minutes, stirring often.
Adjust for salt.
Stir in the cheese a bit at a time until it is melted through.
Serve the cheesy grits into bowls, then top with shrimp gravy, andouille and cooked shrimp.
Garnish with red pepper flakes, fresh parsley and green onion.
