Heat oil in a wide 8-quart heavy pot over moderately high heat until hot but not smoking, then sauté onion, celery, bell pepper, and garlic, stirring occasionally, until golden, 10 to 12 minutes.
Add turkey and sauté, stirring occasionally and breaking up large lumps with a wooden spoon, until meat is no longer pink, about 5 minutes. Stir in salt and pepper.
Purée tomatoes with juice, ketchup, molasses, vinegar, Worcestershire sauce, and Tabasco in a blender until smooth.
Add to turkey and simmer, uncovered, stirring occasionally, until sauce is thickened, 25 to 30 minutes.
Serve turkey sloppy joes on split Cheddar buttermilk biscuits.