Step 1: Heat 1 tablespoon of butter and 1 tablespoon of olive oil in a large non-stick skillet over medium-low heat.
Step 2: Add the sliced yellow onions to the skillet. Cook slowly, stirring occasionally, for 25-30 minutes, or until they are deeply golden brown and very soft. Season with a pinch of salt and pepper. Remove from the skillet and set aside.
Step 3: Lay out one large tortilla on a clean work surface. Spread a thin layer of Russian dressing over the entire surface of the tortilla.
Step 4: Arrange a quarter of the pastrami slices on one half of the tortilla, slightly overlapping.
Step 5: Top the pastrami with a quarter of the caramelized onions, followed by a quarter of the drained sauerkraut.
Step 6: Place a slice of Swiss cheese over the sauerkraut.
Step 7: To roll, fold in the sides of the tortilla over the filling, then starting from the bottom, tightly roll the tortilla upwards to create a secure wrap. Repeat with the remaining ingredients to make four wraps.
Step 8: In the same skillet, melt the remaining 1 tablespoon of butter over medium heat.
Step 9: Place two of the assembled rolls into the skillet, seam-side down first. Cook for 3-4 minutes per side, or until the tortilla is golden brown and crispy, and the cheese is melted and gooey.
Step 10: Carefully remove the cooked wraps from the skillet and slice them in half diagonally. Repeat with the remaining two wraps. Serve immediately.