Lay both puff pastry sheets out flat on a piece of wax or parchment paper. Spread half the cream cheese mixture over each sheet. Then sprinkle half the shredded chicken, half the shredded cheese, and 1/4 cup cilantro over each sheet. One at time, tightly roll each pastry sheet into a log. Wrap both rolls in the parchment paper and freeze for 15 minutes only, to firm the pastry slightly.