Make the Russian dressing: In a small bowl add the mayonnaise, ketchup, sweet pickle relish and ground horseradish. Stir to combine and set aside.
Warm the tortillas: Heat a cast iron skillet or sauté pan over medium high heat. Add the the tortillas 1 or 2 at a time. Heat for 30 seconds per side or until browned in spots. Alternately, heat the tortillas over a gas flame for 10-15 seconds per side. Place in a tortilla warmer or under a damp paper towel.
Make the tacos: For each taco add some shredded corned beef, sauerkraut, cabbage, shredded Swiss cheese and Russian dressing to a warm tortilla.
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Notes
How to reheat corned beef: Reheat cooked corned beef in a microwave safe dish lightly covered with plastic wrap or a paper towel. Heat at 60 percent power for 1 minute. Continue heating at 30 second intervals until heated through. Alternately, heat in a hot skillet stirring frequently until the meat is warmed.How to make Irish tacos in advance: All of the components of the tacos including the corned beef, Russian dressing and shredded cheese can be prepped up to 4 days in advance. But I don't recommend assembling the tacos in advance. They're the best and tastiest when freshly assembled just before serving.Nutritional information is an estimate and based on the ingredients and cooking methods used in this recipe.