Heat a large Dutch oven with a tight-fitting lid over medium-high heat. Pour in enough oil to fill the pan about 1/4-inch deep. Spread flour out on a plate or piece of wax paper. Season half the beef generously with salt and pepper, then dredge in the flour. Shake off the excess flour, and add to the pan. Saute the meat, uncovered, stirring only occasionally, until well-browned, about 8 minutes. Using a slotted spoon, transfer the beef to a plate. Repeat with the remaining beef. Discard the oil and wipe out the pan.
Preheat the oven to 275 degrees F. Return the pot to the stove and melt the butter over medium high heat. Add the onion and cook, stirring, until lightly browned, about 5 minutes. Add the garlic and cook, stirring, until fragrant, about 1 minute. Add the tomato paste and cook, stirring, until lightly browned, about 1 minute more. Return the beef to the pot and add the water or broth, and bring to a simmer. Using a piece of kitchen twine, tie together the parsley, thyme, and bay leaves and add the bundle to the pot. Season with 2 teaspoons salt and pepper to taste. Cover and transfer to the oven. Stew the meat until tender, about 1 1/2 hours.
Remove the Dutch oven from the oven. Skim the fat from the cooking liquid with a ladle. Add the potatoes, carrots, celery, and the tomatoes, and bring to a simmer. Stew, uncovered, on top of the stove, stirring occasionally, until the liquid has thickened and the beef and vegetables are tender, about 1 hour. Remove and discard the herb bundle. Stir in the vinegar and season with salt and pepper to taste. Divide among bowls and serve immediately.
Cook's Note: Beef chuck, because of its marbling of intra-muscular fat, is the choice for any type of stew. If you can't find chuck cubed for stew in your meat department, buy a thick steak and cut it into 2-inch cubes.