Preheat oven to 350 degrees F. Heat olive oil in a large Dutch oven over medium-high heat. Season the short ribs generously on all sides with salt and pepper. Working in batches, brown the short ribs on all sides, 8 to 10 minutes per batch. Transfer seared short ribs to a large plate. Continue the process for the remaining rib batches.
Pour off all but 2 tablespoons of drippings from the pot. Add in the chopped onions, celery, and carrots along with salt and pepper. Cook over medium-high heat with occasional stirring for 3-5 minutes, or until onions are browned. Add in tomato paste and All-purpose flour. Stir well. Allow to cook, stirring occasionally, until deep red about 2 to 3 minutes.
Stir in the red wine along with the short ribs and any accumulated juices. Bring the pot to a boil, then lower the heat to a medium and cook until the wine is reduced by half, approximately 25-35 minutes.
Add the herbs, garlic, and beef stock to the Dutch oven. Stir well. Bring to a simmer, cover, and transfer to oven.
Cook short ribs until the meat easily falls off the bone, 2½ -3 hours.
Transfer the ribs to a large serving plate. Strain the sauce from the pot (Note: The short ribs could be served right out of the pot, but the vegetables have already served their purpose and no longer container the flavor and texture). Separate the fat from the sauce and discard the fat. Drizzle the sauce over the short ribs and serve hot.