Crumble beef into a wide 3- to 4-quart pan over medium heat; cook, stirring, until browned (10 to 15 minutes).
Add up to 2 tablespoons oil, if necessary; or spoon off and discard all but 2 tablespoons of the fat.
Add mushrooms, onions, bell pepper, and oregano; cook, stirring often, until onion is soft and lightly browned (about 10 minutes).
Meanwhile, in a 5- to 6-quart pan, cook spaghetti in 3 quarts boiling water just until tender to bite (10 to 12 minutes); or cook according to package directions.
Add spaghetti and barbecue sauce to beef mixture; mix lightly, using 2 forks, just until heated through.
Sprinkle with parsley.