Cut the meat with the grain into 1/2-inch-thick slices and season on both sides with salt and pepper. Put the flour into a pie pan. Dredge the pieces of meat on both sides in the flour. Tenderize the meat, using a needling device, until each slice is 1/4-inch thick. Dredge in the flour again and set aside.
Add enough of the vegetable oil or bacon fat to just cover the bottom of a 4- to 5-quart Dutch oven set over medium-high heat. Once the oil begins to shimmer, add the steaks to the pan, being careful not to overcrowd. Cook until golden brown on both sides, about 2 minutes per side. Remove the steaks to a plate and repeat until all of the steaks have been browned.
Remove the last steaks from the pot and add the chicken broth and thyme and whisk until the liquid just comes to a boil. Return the steaks to the pot, making sure they are all submerged in the liquid. Cover the pot and place it in on the middle rack of the oven. Cook until the meat is tender and falling apart, 1 1/2 to 2 hours.