In measuring cup, pour boiling water over porcini mushrooms; let stand for 20 minutes. Strain, reserving liquid. I like to strain the liquid through a paper towel lined sieve, because of the sand in the liquid from the mushrooms. Set mushrooms and liquid aside.
Cut ribs into 2 bone pieces. Broil, turning once, until browned, 5 minutes. Place in slow cooker.
In skillet, heat oil over medium high heat; sauté porcini and button mushrooms, onions, garlic, carrots, rosemary, salt and pepper until softened, 5 minutes. Scrape into slow cooker. Add tomatoes.
Whisk together soaking liquid, wine and tomato paste; pour into slow cooker. Cover and cook on low for 7 to 8 hours or until meat is tender. Skim off fat.
In small bowl, whisk together flour, vinegar and 1/3 cup water; whisk into slow cooker. Cover and cook on high for 15 minutes or until thickened. Stir in parsley. Makes 6 to 8 servings.
VARIATION: Stove Top Short Ribs in Red Wine Sauce: Follow recipe as directed, using Dutch oven instead of slow cooker; cover and simmer over medium low heat until ribs are tender, about 2 hours. Skim of fat. Reduce flour to 2 tablespoons and water to ¼ cup; whisk into pan and simmer until thickened, about 5 minutes. Stir in parsley.