Place the pork shoulder chunks in the slow cooker. Add the onion, garlic, carrot, crushed tomatoes, beef broth, oregano, rosemary, salt, and pepper. Stir to combine everything evenly.
Cover and cook on low for 8 hours until the pork is very tender and shreds easily with a fork.
About 30 minutes before the ragu finishes, bring the chicken broth to a boil in a medium saucepan. Slowly whisk in the polenta.
Reduce heat to low and cook the polenta for 20 to 25 minutes, stirring often until thick and creamy. Stir in the Parmesan cheese and butter until melted and smooth.
Shred the pork directly in the slow cooker and stir it into the sauce. Spoon the ragu over bowls of polenta and sprinkle with fresh parsley before serving.