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Preheat oven to 350 degrees F.
In a large dutch oven or oven safe pot with a lid, heat one tablespoon of oil over medium high heat. Add onion and carrots and cook for a few minutes, stirring constantly. Remove veggies to a plate.
Season the ribs with salt and pepper and coat on all sides with flour. Add 2 more tablespoons of oil to the pot and turn heat to high. Add ribs and brown on all sides, about 45 seconds per side. Remove to a plate.
Add the wine to deglaze the pan. Scrape the bottom of the pan to release any browned bites of flavor. Bring to a boil and cook 2 minutes.
Add beef broth, salt and freshly ground black pepper. Stir in tomato paste. Taste broth and add additional seasonings, if needed.
Add ribs, veggies, and (whole) sprigs of thyme and rosemary to the pot.
Cover with the lid and place into the oven. Cook at 350 degrees for 2 hours, then reduce heat to 325 degrees and cook for an additional 30 to 45 minutes. Ribs should be very tender, nearly falling off the bone.
Remove the pan from oven and allow rest for 20 minutes, with the lid on, before serving. Skim off any fat that has risen to the top of the liquid, before serving.
Serve ribs over mashed potatoes with a spoonful of gravy from the pot.
Store leftover short ribs in a sealed container in the refrigerator for 3-4 days depending on the freshness of your ingredients.