Preheat the oven to 350°F.
Heat a large Dutch oven over medium heat. Add the olive oil and heat until very hot.
In a shallow bowl or plate combine the flour with salt and pepper and dredge the shanks in the seasoned flour. Shake the shanks to remove any excess flour, then transfer shanks to the pot and cook until well-browned on all sides, working in batches if necessary, 6 to 8 minutes.
Remove the shanks and set aside.
In a Dutch oven, with a lid, add the onions, celery and carrots to the Dutch oven and cook until softened and lightly browned around the edges, 4 to 6 minutes.
Add the garlic, bay leaves, thyme, rosemary, salt and pepper and tomato paste and cook for 1 minute.
Deglaze the pot with the red wine, scraping up any browned bits from the bottom of the pan. Add the stock, and bay leaves, and bring to a boil on the stovetop.
Return the meat to the Dutch oven, nesting them together; add the bay leaves. Cover the Dutch Oven and transfer to the oven. Cook for about 2 1/2 hours, or until the shanks are very tender.
To finish the recipe, I remove the bay leaves (of course). Taste the sauce and add salt and pepper, to taste. To thicken the sauce, I use about 2 Tablespoons of cornstarch, whisked with about equal water. It is SLOWLY added in, a bit at a time, until it reaches the thickness that I like.
Serve immediately, 1-2 shanks per person. Serve with either orzo, polenta or my personal favorite—Risotto.