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Put the onion slices in a glass bowl and gently pull them apart with your fingers until you have a lot of individual rounds. Add the red wine vinegar and sugar. Use your fingers to coat the onions with the vinegar. Press them down into the bowl and cover with plastic wrap. Set aside to marinate until ready to serve.
Heat 2 cast iron skillets large enough to hold the steaks. Add 2 tablespoons of the oil to each pan. When the oil begins to smoke lightly, season the steak lightly with salt and use a pair of metal tongs to gingerly put the steaks in the hot oil. Cook over high heat, 2 to 3 minutes, on the first side. If the steak becomes overly brown, lower the heat slightly as it cooks. Turn the steak on the second side and cook 2 to 3 minutes. Remove the steak and allow it to "rest" on a flat surface, 10 minutes. Cooks Note: If you like your steak a little more cooked, simply leave it in the skillet a few minutes longer on each side. Wipe out the skillets and use them to warm the tortillas, 1 at a time, over low heat. Alternatively, "char" the tortillas for a few seconds on an open flame.
Preheat the oven to 250 degrees F.
Slice the steak, against the grain, into thin slices. Put a tortilla on a flat surface. Arrange some of the meat, the tomato mixture, cheese and pickled onions in an even line in the center of the tortilla. Remember that the best tasting burritos are ones that have a mix of all the different flavors in the fillings in each bite. Fold the edges into the center and roll it up, pressing as you roll to help keep its shape. Keep it warm on a plate in the oven whole you roll the others. Remove the burritos from the oven and serve immediately.