Bring the beef to room temperature. Allow the chuck roast to sit out at room temperature 30 minutes prior to cooking. This will ensure even browning and cook time.
Season the chuck roast. Preheat an oven to 350°F (177°C). Pat the beef dry on all sides with paper towels, then season generously with about 3-4 tsp Kosher salt and as much black pepper as you like.
Brown the beef. Heat 2 Tbsp neutral oil over medium-high heat in a large Dutch oven or pot with deep sides. Allow this to heat up for a few minutes. Once hot, add the seasoned chuck and cook for about 4 minutes per side. Use tongs to carefully transfer to a plate. Do not drain the grease.
Sauté the aromatics. To the pot, add 1 chopped onion and 2 sliced leeks. Season with ½ tsp Kosher salt, then cook, stirring occasionally, until softened, about 3-4 minutes. Add 4 cloves chopped garlic, then cook 1 minute more. Add 2 Tbsp tomato paste, then use a spatula to break it up as you stir it into the veggies.
Deglaze with wine. Pour in 2 cups red wine, then use a spatula to scrape up any browned bits from the bottom of the pot. Allow this to simmer for about 2-3 minutes.
Add remaining sauce ingredients. Pour in 2 cups low-sodium beef broth, 2 Tbsp low-sodium soy sauce, 2 tsp Dijon mustard, 2 bay leaves, and fresh herbs. I like to tie the herbs together with kitchen twine to make for easier removal later, but this is optional. Stir in the chopped carrots.
Return the beef. Nestle the chuck roast back into the pot. You want there to be enough liquid that the beef is about ⅔ submerged in the liquid.
Cook until tender. Cover with a tight fitting lid, transfer to the preheated oven, then cook until the meat is fork tender, about 3 hours, then remove.
Shred the beef. Carefully uncover the pot, then use a spoon to remove any fat or scum that accumulated at the top. Transfer the braised beef to a cutting board. Allow it to rest until it’s cool enough to handle, then use two forks or tongs to pull the meat.
Finish, then serve! Remove and discard the herbs and dried bay leaves. Taste and adjust seasoning as needed. If desired, you can strain the vegetables, but I like to keep them in. When ready, spoon the red wine braised beef over creamy mashed potatoes or polenta. Serve with some of the braising liquid and tender braised vegetables on top. Garnish with thinly sliced chives and a generous pinch of flaky sea salt. Enjoy!