Generously season the ribs with salt and pepper and coat on all sides.
Preheat oven to 350 degrees F.
In an oven safe pot with a lid, add two tablespoons of oil over medium heat. Add the chopped celery, onions and carrots and sauté for a few minutes, stirring constantly until onion is translucent. Remove veggies to a plate & set aside.
Add 2 more tablespoons of oil to the pot and turn heat to high. Add ribs and brown on all sides, about 45 seconds per side. Remove the ribs & set aside.
Add the wine to deglaze the pan & boil for approximately 2 minutes.
Add the tomato sauce & chicken broth, let that simmer together for 5 minutes before adding back the ribs & veggies.
Cover with the lid and place into the oven. Cook at 350 degrees for 1 hour 45 minutes, then reduce heat to 325 degrees and cook for an additional to 45 minutes. The short ribs should be very tender, almost falling off the bone.
Remove the pan from oven, with the lid on, let it rest for at least 15-20 minutes. Serve ribs with mashed potatoes & garnish with freshly chopped chives. Pour the gravy from the pot overtop.