Sprinkle ribs with salt and pepper, then sear in hot oil in a skillet over medium-high heat. This will take about 7 minutes; do it in batches so the ribs have plenty of room. Place in a 5 quart slow cooker.
Remove most of the fat from the skillet, leaving 1 tablespoon. Cook onion and garlic in remaining fat over medium heat for 4 minutes, then add tomatoes and wine. When the liquid boils, pour over ribs in the slow cooker.
Cook on LOW for 6 hours. Remove ribs and cover with foil on a plate.
Pour pan juices into a saucepan and take out any fat you can see on the surface. Bring to a boil over medium-high, and simmer to reduce to 1 cup. Add tomato paste, sprinkle salt and pepper to taste, and serve over ribs.