Melt the butter and oil in a large saucepan set over medium heat.
Add the onion, bell pepper, and celery. Sauté for 7 minutes until the vegetables are tender.
Add the garlic and sauté for 30seconds.
Gradually add the flour and stir for one minute to make a roux.
Stir in the brown sugar, paprika, thyme, salt, black pepper, and cayenne pepper
Add the green onions, parsley, and broth. Season with additional salt if needed.
Bring the sauce to a boil, reduce the heat to medium-low. Simmer, uncovered, for 20 minutes.
Add the shrimp and cook for an additional 8-10 minutes until shrimp are pink and heated through.
Serve over cooked rice.