Heat the olive oil in a large skillet over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the diced onion and minced garlic to the skillet. Cook for 3 to 4 minutes until the onion softens.
Stir in the red wine vinegar and let it bubble for 30 seconds. Pour in the tomato sauce and beef broth, then season with salt and pepper.
Bring the mixture to a simmer and cook uncovered for 10 minutes, stirring occasionally.
While the sauce simmers, cook the egg noodles in a separate pot according to package directions. Drain them well.
Stir the chopped basil into the beef mixture. Add the drained noodles and toss gently to combine everything.