Sprinkle short ribs generously with salt and black pepper and rub into the meat using your hands. Sprinkle the short ribs with flour and turn gently to coat meat entirely. Set aside.
In a large dutch oven or heavy bottomed pot, preheat oil over medium to medium high heat. Add 3-4 short ribs to your pot and brown of all sides. Remove from pan and brown remaining short ribs, adding more oil if needed. Remove and set aside.
While short ribs are browning, place onion, carrot and celery into the bowl of a food processor and pulse into a fine paste.
Add more olive oil and finely pulsed veggies into pot. Saute 8-10 minutes or until tender.
Turn heat completely off and pour in red wine. Bring to a boil. Turn heat back on and simmer 5-7 minutes or until the liquid is reduced by half.
Pour in beef broth, rosemary, thyme, bay leaves, crushed tomatoes, salt, black pepper, and browned short ribs. Bring entire pot to boil and then turn heat down to a low heat or to where the pot can remain at a light simmer.
Partially cover pot and cook about 5 hours, stirring every 30 minutes or so. After about 3 hours, taste the broth and adjust salt. Ribs will be done when meat is very tender and falling off the bone.
Serve warm with mashed potatoes and garnish with fresh chopped parsley, if desired.