Preheat the oven to 325°F.
Sprinkle the ribs with salt on all sides. Dredge in flour until well coated.
Heat the olive oil in a Dutch oven or braiser over medium-high heat. Add the ribs, browning on all sides, remove and set aside.
Add the leeks, celery, and carrots, lower the heat to medium. Cook until the vegetables have started to caramelize, about 20 minutes. Stir in the garlic.
Add the balsamic, beer, and broth, scraping to deglaze the bottom of the pan.
Add the ribs back in, along with the tomatoes and tomato puree.
Cover and add to the oven for 2 hours, stirring occasionally.
After 2 hours, remove the lid and continue to cook until fork-tender, about 1 additional hour.
Remove the ribs, set aside.
Add the remaining liquid and vegetables to a blender, blend on high until well combined.
Plate the ribs, drizzle with sauce, sprinkle with chopped parsley.