Chill 8 serving plates. Place meat in freezer about 10 minutes.
Slice cold beef across grain into 1/8-inch slices. Then place each slice, one at a time, between 2 sheets of plastic wrap and, using the smooth side of a meat pounder, flatten by gently pounding and pressing back and forth. Work from center out. Keep turning to flatten it evenly to about 1/16 inch. (You should spend about a minute on each slice.)
Entirely cover each chilled plate with thin slices of beef. (At this stage, you can cover with plastic wrap and reserve in refrigerator for several hours.) Carefully spoon reserved dressing over meat to evenly cover. Garnish with Parmesan strips and chives, and serve immediately.
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