In a large skillet over medium heat, cook the ground beef with the onion, carrots, celery, and garlic until the beef is browned. Drain any excess fat.
Transfer the mixture to the slow cooker. Add the crushed tomatoes, tomato paste, beef broth, oregano, basil, salt, and pepper. Stir to combine.
Cover and cook on low for 6 to 8 hours until the sauce thickens and the vegetables soften.
About 30 minutes before serving, bring the water to a boil in a medium saucepan. Whisk in the cornmeal gradually. Reduce heat to low and cook, stirring often, until thick and creamy, about 15 minutes.
Stir the butter and Parmesan cheese into the polenta until melted and smooth. Spoon the polenta into bowls and top with the Bolognese sauce. Add extra Parmesan if desired.