1 large onion, peeled and thinly sliced (1 1/2 cups)
1 medium carrot, peeled and coarsely chopped (3/4 cup)
1 rib celery, coarsely chopped (3/4 cup)
2 garlic cloves, peeled and thinly sliced
1 dried bay leaf
1/4 teaspoon whole black peppercorns
3 sprigs fresh thyme
FOR BRAISING MEAT
1 tablespoon all-purpose flour, plus more if needed
3 tablespoons red-wine vinegar
2 tablespoons tomato paste
1 1/4 cups water
FOR GARNISH VEGETABLES
3/4 pounds turnips, about 3, peeled and cut into 1 1/2-inch wedges
3/4 pound small new potatoes
3/4 pound carrots, 4 to 5 medium, peeled and cut into 3-inch lengths. Halve thick ends lengthwise, then cut into 3-inch lengths
Pat meat dry with paper towels, then season on all sides with salt and pepper. Heat a Dutch oven over high heat for 2 minutes. Then add enough oil to barely coat bottom of pot and heat until shimmering. Sear the meat until golden brown, turning to cook all sides evenly, about 8 minutes. Don't be tempted to turn the meat too soon or it will tear; instead wait until it easily releases from the pot. Once it is nicely browned all over, remove it from the pot. If there are lots of blackened bits on the bottom of the pot, wipe it clean with a paper towel, or deglaze with a little water then discard.
Reduce heat to medium. Add the olive oil and all of the aromatics, and cook, stirring fairly often, until the onion is translucent, 2 to 3 minutes. You may need to increase the heat after a minute or two if the onion isn't softening, but only slightly. If the garlic or onion begins to burn, add a little water and stir up the browned bits from the bottom of the pan.
Sprinkle the flour into the pot, and stir to coat everything evenly; cook the flour just long enough to remove the starchy taste without taking on any color, about 30 seconds. Add vinegar, tomato paste and water, and bring to a boil. Deglaze pot, scraping up browned bits from the bottom. Put the roast in the pot; the water should come only about 1 inch up the sides of the meat. Reduce the heat so the liquid is simmering, not boiling, and cover the pot tightly with the lid. While the meat is braising, turn it every 30 minutes; the meat should be almost tender (a sharp knife inserted in the center should meet little resistance) after 2 1/2 to 3 hours. Remove the meat from the pot. Strain braising liquid through a fine sieve, pressing on the solids to extract as much liquid as possible (discard solids).
Return the roast and the strained liquid to the pot. Nestle the garnish vegetables around the roast, submerging them a bit in the liquid (the liquid should almost reach top of vegetables). Bring the liquid to a boil, then simmer until the vegetables are tender, 15 to 20 minutes. The meat should be very tender by now and give no resistance when pierced with a knife (The meat will be firm enough to slice; if you want it be falling-apart tender, cook 30 minutes more).
Transfer the meat and vegetables to a serving platter, leaving the sauce behind (there should be about 1 cup). Cover and keep warm near the stove. If the sauce is too thin, heat until reduced (but be mindful of the saltiness, since the more sauce is reduced the saltier it will taste) or thicken it with a bit more flour, whisking until smooth. Add a small amount of vinegar if necessary to balance the flavors. Let roast stand for about 20 minutes, then slice to desired thickness. Spoon some sauce over pot roast and vegetables to moisten and serve with remaining sauce on the side.