Season the chuck roast with the salt and the black pepper.
Heat a large Dutch oven over high heat, about 2 minutes.
In the heated Dutch oven, add enough of the extra olive oil to barely coat the bottom and heat until it is shimmering.
Add the seasoned chuck roast to the heated olive oil and sear, turning occasionally, until it is golden-brown on all sides, about 8 minutes.
Place the seared chuck roast on a large plate and wipe the Dutch oven clean.
In the same Dutch oven over medium heat, add the remaining 1 tablespoon of the olive oil, the onions, 3/4 cup of the chopped carrots, the celery, the garlic, the bay leaf, the black peppercorns, and the thyme and cook, stirring frequently, until the onions are translucent, about 2-3 minutes. If the garlic or the onions begin to burn, slightly lower the stovetop heat, add a small amount of the extra water, and stir to loosen the browned bits from the bottom of the pan.
Add the flour to the onion mixture and cook, stirring constantly, until it is evenly coated and is just cooked enough to remove the starchy taste without taking on any of the color, about 30 seconds.
Add the red wine vinegar and the remaining 1 1/4 cups of the water to the onion mixture and stir to loosen any of the browned bits from the bottom of the Dutch oven.
Bring the onion mixture to a boil, stirring constantly.
Add the seared chuck roast to the onion mixture. The liquid should come up about 1-inch on the sides; add more of the extra water if it does not. Reduce the heat to a simmer.
Tightly cover the Dutch oven and simmer the chuck roast in the onion mixture, turning every 30 minutes, until the meat reaches an internal temperature of 145 degrees F and is tender, about 2 hours 30 minutes-3 hours.
Place the chuck roast on a large plate.
Strain the braising liquid over the meat through a fine-mesh sieve, pressing on the solids to extract as much of the liquid as possible. Discard the solids.
In the same Dutch oven, add the chuck roast and the strained braising liquid.
Closely nestle the turnips, the potatoes, and the remaining carrots around the chuck roast, pushing down on the veggies to almost completely submerge them in the liquid.
Set the Dutch oven over medium-high heat and bring to a boil.
Reduce the heat to medium-low. Simmer the pot roast until the vegetables are tender and the meat is very tender, about 15-20 minutes.
Transfer the pot roast to a serving platter and let it stand, about 15-20 minutes.
Slice the pot roast and serve drizzled with its cooking liquid.