Place potatoes in a large pot of boiling, salted water and cook until soft. (Be careful not to overcook.) Drain very well and allow to cool.

Meanwhile, sauté onions in oil until soft and slightly browned. Place cooked potatoes and onions into a large mixing bowl and mash until smooth and creamy. Add beaten egg, reserving one tablespoonful for glazing puffs, and salt and pepper, to taste. Set aside.

Preheat oven to 350 degrees (175 degrees Celsius). Line a baking pan with Gefen Parchment Paper.

Working with one slice at a time, lay out the pastrami slices and trim to one- and one-fourth-inch (three-centimeter) strips. Dice shavings and sauté in a bit of oil; add to potato mixture and stir to combine. Using two strips of pastrami per puff, place strips one over the other, forming an X shape. Place a large scoop of potato mixture in the center of the X and cross pastrami ends over the top of the scoop, folding over and pressing down. Turn over and place seam-side down on the prepared baking pan. Repeat with remaining pastrami and potato mixture. Glaze with reserved egg and bake for 25 minutes.

Sauté onions in oil until caramelized. Add remaining ingredients and mix well; bring to a boil. Lower heat and simmer for five minutes, stirring until slightly thickened. Divide evenly over potato puffs and serve.