Melt butter and oil in a heavy bottomed pan over medium heat. Once the butter melts, add half the flour and whisk until smooth. Repeat with the remaining flour.
Continue to cook the roux, stirring constantly, until it turned light brown –about the color of peanut butter.
Add the diced onion, green bell pepper, celery, garlic, green onions, tomato paste, seasoning and cayenne pepper, if using.
Add the shrimp or chicken stock. Keep stirring until the roux is dissolved into the broth.
Bring the pot to boil, then reduce the heat to medium low to low. Cover the pot and allow the étouffée to simmer for 45 minutes, stirring every 15 minutes.
Add the crawfish tails and shrimp. Simmer until the meat is heated through, about 6-8 minutes.
Season with salt and pepper to taste.
Serve étouffée over white rice and garnish with additional diced green onions.