To a food processor, add the onion and garlic then pulse until minced, or finely mince by hand. Heat the oil in a large skillet with high sides over medium heat then add the onions and garlic and saute until softened, 5 minutes.
Meanwhile, add the carrots, celery, and mushrooms to the food processor then pulse until minced, or finely mince by hand. Add to the skillet then turn the heat up to medium-high. Season the vegetables with salt and pepper then saute until tender, 5-7 minutes.
Add the ground beef to the skillet, season with salt and pepper, then saute until the beef is no longer pink, breaking it up finely as it cooks. Add the marinara sauce and chicken broth to the skillet then stir to combine, turn the heat down to medium, place a lid partially on top, and simmer for 10 minutes, stirring occasionally. Stir in fresh basil then taste and add salt and pepper if necessary.
Meanwhile, bring a large pot of salted water to a boil then add the spaghetti and cook until it's all dente. Drain then scoop into bowls, top with the vegetable ragu, and then serve.