Prepare all ingredients by trimming the beef, dicing the vegetables, and mincing the garlic.
Brown the beef in a skillet with olive oil, seasoning with salt and pepper, then transfer to the slow cooker.
Sauté the diced onion, carrots, and celery in the same skillet for about 5 minutes, then add minced garlic and cook for an additional minute. Transfer to the slow cooker.
Add crushed tomatoes, beef broth, tomato paste, oregano, basil, red pepper flakes, and bay leaf to the slow cooker. Stir to combine.
Cover and cook on low for 480 minutes or on high for 240 minutes.
Cook pasta according to package instructions about 30 minutes before serving. Shred beef and stir back into the sauce before serving over pasta.