Preheat your oven to 325. Heat a large Dutch oven over medium high heat.
Season the ribs all over with salt and pepper.
Place a small amount of oil in your pan and place the ribs in the pan, being careful you don't crowd them. Brown the ribs on all sides, about 3 minutes per side. The trick to searing is: do not move the meat! It will let you know it's ready to be turned when you nudge it gently with tongs and it lets go of the pan.
When all of the meat is browned, remove it to a plate and add the onion, carrots and celery to the pan. Cook for about 5-7 minutes, or until the veggies are just beginning to brown.
Add the tomato paste and cook - it will stick to the brown bits on the bottom of the pan, but that's exactly what you want. You want the tomato paste to turn completely brown. When this happens, about 4 minutes or so, add the garlic, and then deglaze the pan with the red wine, scraping up all of the brown bits.
Add the tomatoes and the chicken stock.
Place the ribs back into the pan, nestling them down into the liquid. Cover loosely with foil and place in the oven, Cook for an hour, the turn the ribs over and cook another hour. These ribs take about 2-3 hours to cook, depending on the beginning size. They are done with they begin falling apart and off the bone.
When the ribs are done, remove them to a plate and strain the cooking liquid through a strainer - it doesn't have to be perfectly strained, a colander is fine. Discard the solids and place the sauce and ribs back in the pan and keep warm until serving. The liquid makes a nice thick sauce which doesn't need any sort of butter mounting or anything, it's rustic.