Heat the olive oil in a large deep skillet or sauté pan over medium-high heat. Add the ground beef, season with salt and pepper, and cook for 5 to 7 minutes, breaking it up as it cooks, until browned and cooked through. Use a slotted spoon to transfer the beef to a plate, leaving a little drippings in the pan.

Add the onions to the same pan and cook for 3 to 4 minutes until softened. Add the mushrooms with a pinch more salt and cook for 6 to 8 minutes, stirring occasionally, until golden and their moisture has cooked off.

Sprinkle the flour over the onion and mushroom mixture and stir for 1 minute to coat and cook off the raw flour taste. Gradually whisk in the beef broth, scraping up any browned bits from the bottom of the pan. Stir in the Worcestershire sauce and bring to a gentle simmer until the sauce begins to thicken.

Return the browned beef to the pan and add the egg noodles, stirring to make sure the noodles are mostly submerged in the sauce.

Simmer uncovered over medium heat for 10 to 12 minutes, stirring occasionally, until the noodles are tender and the sauce has thickened into a rich gravy. If the pan looks dry before the noodles are done, add more broth or water a quarter cup at a time. Stir in the vinegar, taste, and adjust seasoning with more salt and pepper as needed. Garnish with fresh parsley and serve warm.