- Tie a piece of kitchen twine around the circumference of the roast; tie it tight like a belt. Tie a few pieces of twine over and around the top of the roast to compact it for even cooking. Pat the roast dry with a paper towel and generously season both sides with salt and pepper. Heat a 4- quart Dutch oven over medium-high heat. Add enough grapeseed oil to generously cover the bottom of the pot. When the oil is hot, add the roast; you should hear it sizzle immediately. Sear the meat on one side without disturbing it for about 4 minutes; you want to develop a deep brown color right out of the gate.
- Transfer the meat to a cutting board and return the pot to the heat for 30 seconds; this gives the pot a chance to recover heat so both sides of the roast will be evenly and deeply browned and caramelized. If the pot looks dry, add a little more oil to cover the bottom and, when the oil is hot, return the meat to the pot, browned side up. Slightly tilt the pot and, using a large spoon, baste the topside of the roast with the hot oil and juices. This will help to brown all the little pockets and crevices in the roast. Continue this process of removing the meat, letting the pot get hot, then returning the meat to the pot and basting it until all sides are deeply browned, 5 to 8 minutes. Transfer the roast to a plate, tent with foil, and set aside. Pour the cola into the pot, crank the heat up to high, and bring to a rapid boil. Add the veal demi-glace, chicken stock, 1 tablespoon of salt, 2 teaspoons of black pepper, and the Espelette pepper, and return to a boil. Cut the heat down so that the liquid simmers aggressively and cook until the liquid reduces in volume by half, about 30 minutes.
- Rearrange your oven racks so the Dutch oven will slide in and out easily. Preheat the oven to 350°F. Cut a 20-inch square of cheesecloth and lay the carrots, celery, and onion in a single layer in the center. Gather the corners together over the vegetables and tie the packet closed with a piece of twine. This packet makes it easy to pull the vegetables from the pot roast when the cooking is done.
- Transfer the roast back to the pot and top with the single-layer vegetable packet. Pour the reduced braising liquid over the top; it should just cover the roast and the vegetables (add more stock if needed). Slide the pot into the oven and cook, uncovered, for 2 hours. Check the roast every 30 minutes or so, pressing the vegetables down into the braising liquid. After 2 hours, put the lid on the Dutch oven and continue cooking another hour, for a total cooking time of 3 hours.
- Pull the pot from the oven and remove and discard the cheesecloth bundle. Cut, remove, and discard the twine. Put the roast back into the Dutch oven, put on the lid, and keep warm until ready to serve.
- Transfer the roast to a warm, shallow platter and tent with foil. Measure out 4 cups of the braising liquid and pour the remaining braising liquid into a separate bowl. Return the 4 cups braising liquid to the pot and bring to a rapid boil over medium-high heat. Boil until the liquid reduces in volume by half, about 5 minutes. Remove the pot from the heat and whisk in the butter. Spoon the sauce over and around the roast and sprinkle with the chives. Store the remaining braising liquid with any leftovers.
- Fill a 2-quart saucepan three-quarters full with water and bring to a rapid boil. Fill a large bowl with ice water. Line a baking sheet with a clean, dry kitchen towel.
- Peel the turnips, rutabaga, beets, and carrots. Cut each into 3⁄4-inch dice and pile in separate mounds on the towel. Wash and cut the (unpeeled) sunchokes, (unpeeled) new potatoes, and celery into 3⁄4-inch dice.
- Drop the turnips and potatoes into the boiling water and blanch for 4 minutes. Using a spider strainer or slotted spoon, transfer the vegetables to the ice bath and swirl to cool. Transfer to a section of the towel to drain. Using the same cooking, cooling, and draining method, blanch the carrots and sunchokes for 2 minutes each. Lastly, blanch the beets and rutabagas for 6 minutes each. You blanch the beets and rutabagas last because they release some color into the blanching water that would stain the other vegetables. Celery does not need to be blanched because it is the least dense of the vegetables and will cook quickly.
- Evenly spread the turnips, potatoes, carrots, sunchokes, beets, and rutabagas in a deep 12-inch sauté pan. Add the chicken stock and bring to a boil over high heat. Scatter the celery over the top of the vegetables. Cut the heat down to medium and let every- thing simmer aggressively until the vegetables are fork-tender and almost all the liquid is gone, about 8 minutes. Pull the pan from the heat and swirl in the butter, ½ teaspoon salt, and about 6 grinds of black pepper.