Season beef shanks generously with salt and pepper. Brown in a dutch oven on medium-high heat on all sides. Remove from pot and set aside.
Add vegetable oil and onions, celery and carrot. Cook for several minutes until onion has turned translucent and celery and carrot have softened.
Stir in flour and tomato paste. Cook for several minutes or until flour is no longer raw.
Add red wine and bring to a boil.
Return beef shanks to dutch oven and lower heat to a simmer. Cook uncovered for 20 minutes or until liquid has reduced by half and alcohol has cooked off.
Add in seasonings and beef stock.
Cook covered for 2-3 hours in the oven at 350 degrees. Serve when tender and meat is coming off the bone. To create a sauce, spoon out some of the braising liquid and reduce in a small pot. Add a slurry of cornstarch to thicken, then serve over the beef shanks. Enjoy!