Heat olive oil in a large skillet over medium heat.
Add chopped onion, carrots, and celery to the skillet and cook for 5-7 minutes until softened.
Add minced garlic and cook for 1 minute more until fragrant.
Add ground beef to the skillet and cook, breaking it up with a spoon, until browned and no longer pink, about 6-8 minutes.
Transfer the cooked beef and vegetable mixture to the slow cooker.
Pour the red wine into the skillet and scrape the bottom to loosen any browned bits, then add the wine to the slow cooker.
Add crushed tomatoes, tomato paste, dried oregano, dried basil, dried thyme, salt, black pepper, and red pepper flakes to the slow cooker. Stir to combine.
Pour in the whole milk and beef broth and stir again to combine all ingredients.
Cover and cook on low for 6 hours, stirring occasionally if possible.
After cooking, taste and adjust seasoning with additional salt and pepper if needed.
Serve the bolognese sauce hot over cooked pasta or as desired.