First, brown the beef: Heat a large skillet over medium heat. Add a tablespoon of olive oil, and then the ground beef. Break up any large clumps with a wooden spoon, and cook until it's no longer pink, about 8 minutes. (To make the sauce vegan / vegetarian, simply omit this step).
Meanwhile, heat a separate large skillet over medium heat. Add a tablespoon of olive oil, then the onion, celery, carrots, mushrooms, garlic, and oregano. Sauté for 5-7 minutes, until everything is soft.
Reduce the heat of the veggie pan to low, then add the tomato sauce, parsley, and the cooked beef once it's ready. Mix well, and simmer for at least 5 minutes. Season with salt and pepper to taste, if needed.
Pour the sauce over your favorite pasta or zucchini noodles, and garnish with more fresh parsley.