Preheat your oven to 325°F (160°C). Pat the beef chuck roast completely dry with paper towels. Season generously on all sides with salt and pepper.

Heat the olive oil in your Dutch oven over medium-high heat on the stovetop. Sear the roast for 3-4 minutes per side, until a deep brown crust forms. Remove the roast from the Dutch oven and set aside.

Add the chopped onion, carrots, and celery to the Dutch oven. Cook, stirring occasionally, until the vegetables begin to soften and brown slightly, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Stir in the tomato paste and cook for 1 minute, stirring constantly. Pour in the red wine and scrape the bottom of the pot with a wooden spoon to deglaze, loosening any browned bits. Let the wine simmer and reduce slightly for about 2-3 minutes.

Return the seared roast to the Dutch oven. Pour in the beef broth. Add the fresh rosemary, thyme, and bay leaves. The liquid should come about halfway up the sides of the roast. If needed, add a bit more beef broth or water.

Bring the liquid to a gentle simmer on the stovetop. Cover the Dutch oven tightly with its lid and transfer it to the preheated oven.

Braise for 3 to 4 hours, or until the roast is fork-tender and easily shreds. The cooking time will vary depending on the size and thickness of your roast.

Once the roast is tender, carefully remove it from the Dutch oven and place it on a cutting board. Tent with foil to keep warm.

Strain the cooking liquid into a saucepan, discarding the solids (rosemary stems, thyme stems, bay leaves). Skim off any excess fat from the surface of the liquid.

If you prefer a thicker gravy, whisk the 2 tablespoons of flour with 1/4 cup of cold water to create a slurry. Bring the liquid to a simmer in the saucepan and whisk in the slurry until the gravy thickens. Season with additional salt and pepper to taste.

Slice or shred the pot roast and serve it with the rich gravy.