Heat oil and butter in a large saucepan over medium-high heat until shimmering.
Add onions, celery, and bell peppers and cook, stirring occasionally, until vegetables start to soften, 3 to 5 minutes. Stir in garlic, creole seasoning, paprika, thyme, oregano, basil, and black pepper, and cook until fragrant, about 30 seconds.
Stir in tomatoes, chicken stock, hot sauce, and Worcestershire sauce. Bring to a boil, then reduce heat to low. Simmer until sauce slightly thickens, about 20 minutes.
Remove from heat and stir in the green onions. Season with salt, pepper, and additional hot sauce to taste.
Serve with seafood, rice, sausage, or chicken breasts.
Notes
Vegetarian: Make this vegetarian by using vegetable stock in place of chicken stock.
Make ahead tips
The sauce will keep in a sealed container in the refrigerator for up to 1 week.
Or the sauce can be frozen for up to 3 months. Thaw in the refrigerator overnight.