In a large saucepan, heat butter and oil over medium heat. Whisk in flour, and cook, whisking frequently, until a blond roux forms.
Add onion, carrot, celery, tomato, mushrooms, and garlic; cook for 5 minutes. Add stock, wine, bay leaves, and thyme. Season to taste with salt and white pepper; simmer for 20 minutes.
Add crawfish, and cook for 5 minutes. Check seasoning, and add salt and white pepper to taste. Serve with a scoop of hot cooked rice. Garnish with thyme, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/crawfish-fricassee/