Heat 1 tablespoon of oil on a large outdoor griddle, such as a Blackstone, over medium heat.
Add sausage and cook until browned and fat has rendered, about 3 minutes. Add onion, peppers, and celery to drippings. Add 1 teaspoon Cajun seasoning and cook, stirring occasionally until vegetables are tender, about 3 minutes.
Meanwhile, add 1 tablespoon oil to the other side of the griddle. Add tortellini and toss to coat lightly. Add water; cover with a griddle dome and cook for 3 to 4 minutes, uncovering and tossing halfway through.
Push sausage mixture to the side and add remaining oil to the griddle. Season shrimp with Cajun seasoning and add to the oil. Cook, undisturbed 1-2 minutes or until lightly browned. Flip and cook 1 minute longer.
Toss all ingredients together in the center of the griddle until well combined.
Add cream and cook until thickened slightly, about one minute, stirring constantly. Add Parmesan and cook 1 to 2 minutes until creamy and well combined. Squeeze lemon on top and stir in fresh parsley. Serve immediately.
