Cook onion in oil and butter in a 12-inch heavy skillet over moderately high heat, stirring frequently, until onion is softened and browned, about 15 minutes.
Add flour and cook, stirring, 1 minute. Stir in water, broth, Worcestershire sauce, and pepper and simmer, stirring and scraping up brown bits, until gravy is slightly thickened, 8 to 10 minutes. Season with salt and additional Worcestershire sauce if desired.