Set a heavy Dutch oven over medium-high heat, add a drizzle of oil and the butter and brown the ribs on all sides, sprinkling them with salt and pepper.
Remove from the pan, add the onion, celery and carrot and cook for a few minutes, until soft.
Add the red wine and cook until reduced by half; add the tomato paste and cook for another minute.
Return the ribs to the pan, add the beef stock and tomatoes, cover and braise at 300˚F for 3-3 1/2 hours, or until the meat is very tender.
Shred the meat from the bone and simmer the sauce on the stove top, uncovered, if you’d like it to thicken.
Serve over pasta.