In a large, heavy flameproof casserole, preferably cast iron, over medium heat, heat the olive oil and saute the onions until golden. Thoroughly dredge the beef in the flour, covering all the surfaces. Add to the pan and brown on all sides. The flour may cause the onions to burn slightly. This is good and will add lots of flavor. Add the carrots, celery, beef broth, wine, thyme, black pepper, and salt to taste. Reduce heat, partially cover, and barely simmer for 3 to 3 1/2 hours, turning the beef occasionally. Remove the carrots and celery when they are cooked and reserve.

When the beef is falling-apart tende, remove it from the broth. Remove the thyme sprigs. Knead the butter and 2 tablespoons flour together until thoroughly combined. Add the mixture to the broth and stir with a wooden spoon until you have a sauce the consistency of buttermilk. Remove from the heat.

To serve, slice the beef and arrange on a platter. Cover with some of the sauce. Put the remaining sauce in a bowl or gravy boat. Arrange the carrots and celery attractively on the beef platter. Garnish with fresh thyme sprigs, if you like. Serve immediately.