Preheat the oven to 325°
Lightly dust the shanks with the salt and pepper and brown in the olive oil in the Dutch oven over medium heat.
Remove the shanks from the pot, leaving behind the rich browned bits on the bottom.
Add more olive oil if dry, and stir in the chopped veggies. Sauté till they begin to soften.
Push the veggies away from the center and spoon the tomato paste into the space. Continue to sauté that, stirring frequently for a minute or two till fragrant. Mix the veggies into the tomato paste and stir in the thyme and bay leaves.
Pour half the wine into the veggies and simmer, using a wooden scraper to loosen the brown bits on the bottom of the pot. Add the remainder of the wine and continue to simmer, uncovered, till reduced by half.
Pour in the stock and return the shanks to the pot. Cover and bring to a rapid simmer, then carefully move the pot to the preheated oven.
Slow roast for 2 1/2-3 hours, checking after 2 hours for tenderness. The meat should be very tender when finished. Remove pot from the oven.
Using a slotted spoon or tongs, remove the shanks from the pot and set aside. Strain the veggies and bay leaf from the broth and return the broth to the pot. (See note below.)
Bring broth to a simmer. Make a slurry with the cornstarch and water, and whisk into the simmering broth, whisking vigorously as it returns to a simmer. When the sauce is velvety and as thick as you like, then taste it and add salt and/or pepper if needed.
Return the shanks to the sauce and gently heat through. Serve over mashed potatoes, polenta, noodles, rice...your starch of choice...or simply on the plate if you are watching carbs.
Enjoy!