Sprinkle short ribs with salt and pepper on all sides and place into slow cooker.
Top with onions, celery, garlic, thyme, bay leaves.
In a medium bowl, whisk together beer, beef broth, tomato paste, brown sugar, and dijon mustard.
Pour over short ribs.
Cook on low for 8-9 hours or high for 4 hours.
Remove the short ribs from the slow cooker.
Skim the fat off the sauce in the slow cooker, and using an immersion blender, puree the onions and celery into the sauce.
Serve with Parmesan polenta.
To make the polenta:
Add chicken broth and garlic to a medium pot and bring to a simmer.
Whisk in polenta.
Cook, stirring often with a wooden spoon, until thick, about 10 minutes.
Once thickened, add heavy cream, salt, pepper, and Parmesan cheese, stirring to combine.
Serve topped with short ribs, rosemary, and additional Parmesan cheese, and a light drizzle of the sauce.