Dust a flat work surface lightly with flour. Unroll puff pastry sheets; roll each out into a 10×15-inch rectangle. Spread a thin layer of Dijon mustard over puff pastry. Cover mustard with a layer of pastrami slices, followed by a layer of Swiss cheese slices. Roll puff pastry up tightly like a jelly roll. Wrap in plastic wrap and refrigerate for 1 hour, or up to 24 hours.
Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Slice puff pastry rolls into 1/4-inch-thick slices and lay on the prepared baking sheets. Brush tops with beaten egg and sprinkle with caraway seeds.
Bake in the preheated oven until pastry is lightly browned, about 12 minutes. Let sit for 1 minute on baking sheet before removing.