Pour 1 tablespoon of oil into a large skillet and place over medium-high heat.
Brow sausage, about 3 minutes. Remove sausage from skillet and set aside.
Remove all but 2 teaspoons of grease from the pan and add the remaining oil.
Add onions, bell pepper and celery and sauté for 4 to 5 minutes or until onions barely begin to look translucent. Season with salt and pepper.
Stir in garlic, corn and corn milk and continue to sauté for 2 minutes.
Add rice, herbs and spices and sauté for 4 to 5 minutes. Add sausage back into the skillet. Season with salt and pepper.
Stir in crushed tomatoes and stock until well incorporated. Bring mixture to a boil, than reduce the heat to simmer and cover. Cook for about 15 to 20 minutes or until cooked about 2/3 of the way, then add shrimp by gently pressing shrimp slightly into the mixture.
Cover again and continue to simmer for 7 to 10 minutes or until rice as cooked through and the liquid has evaporated.
Gently fluff jambalaya, top with thyme or parsley and serve.