Cut the short ribs crosswise into 2-inch pieces, and season with salt and pepper.

Roughly chop the vegetables. These won’t be eaten, they just flavor the sauce.

In a large Dutch oven, over medium-high heat, heat the olive oil. Sear the short ribs on all slides for 7 - 8 minutes, working in batches. Don’t overcrowd the pan with each batch. Transfer the browned short ribs to a plate, and set aside.

Once all batches are browned, spoon out all but 4 tablespoons of the drippings from the pan. Add the garlic, and cook on medium heat for 1 minute.

Add the remaining vegetables and cook until softened, about 5 - 10 minutes over medium-high heat. Add the flour and tomato paste, and cook for an additional 2 - 3 minutes.

Add the wine and broth, and stir well until combined and cook until reduced by half, about 20 minutes over medium heat.

Preheat the oven to 350°F, and position the oven rack in the center of the oven.

Turn off the stovetop heat, and place the ribs into the Dutch oven. Add in the herbs.

Place the lid on the Dutch oven, and place in the oven to braise for 3 hours. (For safety and quality, check on the short ribs occasionally during this time. Stir gently if needed.)

Once the short ribs are nice and tender, remove them from the oven. With a slotted spoon, remove the short ribs to a plate.

Strain out the vegetables and herbs through a colander, keeping the sauce. Add the ribs back to the Dutch oven, and pour the sauce over with a spoon.

Serve with mashed potatoes or rice, with your favorite vegetables.