In a pan, sauté yellow onions, bell pepper, and celery in 1 tablespoon butter until soft.
Season crawfish tails and fat with salt and pepper, then add to pan. Turn heat to high, stirring continually to avoid scorching. Add remaining butter. Once butter has melted, slowly add flour and stir until smooth to form a roux. Simmer on medium heat, stirring regularly, until roux begins to turn beige, about 15 to 20 minutes. (If you prefer a deeper roux flavor, continue to cook until roux is golden brown or brown. Be careful not to burn vegetables or scorch the pan.)
Add stock and stir until roux has completely dissolved. Add bay leaves, thyme, and Tabasco. Bring pot up to a slow boil for 5 minutes, then reduce to a simmer. Cover and simmer for 20 minutes. The sauce should be thick enough to coat the back of a spoon. Adjust consistency with more stock if necessary.
Adjust seasoning with salt and pepper and, if desired, a bit of lemon juice. Serve over steaming medium-grain rice, garnished with sliced scallions.