Heat oven to 375 degrees.
Season the short ribs and marinate overnight or for at least a couple of hours.
Remove the pieces of garlic from the short ribs and then sear in a Dutch oven on medium heat in olive oil until golden brown on all sides.
Remove from pan and set aside.
Remove rendered fat from the pan and leave about a tbsp for sauteing vegetables.
Add onion, carrots & celery to the pan and sauté for 2 minutes.
After 2 minutes, add the tomato paste and mix and sauté for another 2 minutes.
Add garlic and sauté for 30 seconds until fragrant.
Next, deglaze the pan with red wine and allow it to reduce for 1 minute.
Add broth and stir.
Add short ribs back to the Dutch oven bone side up, ensuring they are nestled comfortably in the braising liquid.
Add fresh herbs to the pot and cover.
Turn off heat and put in the oven at 375 degrees for three hours, checking for tenderness after 2 hours.
After ribs are fork-tender and bones easily slide off the meat, remove from oven and allow the short ribs to rest for at least 10 minutes.
Remove ribs from Dutch oven and shred with two forks, discarding of the membrane and fatty tissue.
Scoop rendered fat off the top of the braising liquid with a large spoon and discard.
Turn the braising liquid back on medium-low heat and add crushed tomatoes to the mixture.
Season to taste with salt, pepper, and a pinch of sugar.
Allow the sauce to simmer and come together for about 10 minutes.
After 10 minutes, add heavy cream, parmesan cheese, and stir.
Finally, add the shredded meat back into the sauce, cover with a lid, turn off the heat off and allow the meat to warm up from the residual heat from the pan.
Meanwhile, cook your bucatini pasta according to box instructions for al dente or desired tenderness.
Drain pasta and combine with meat sauce.
Serve with fresh parsley and lots of Parmesan cheese and black pepper on top.