Preheat oven to 400°F Beat egg and 1 Tbsp water with wire whisk until blended. Set aside. Unfold pastry on lightly floured surface. Roll into 14" x 10" rectangle; cut in half lengthwise. Brush both pastry halves lightly with egg mixture.
Sprinkle 3 Tbsp of the cheese and the pepper evenly over 1 of the pastry pieces; cover with ham slices. Place remaining pastry piece, egg side down, over ham. Brush with additional egg mixture. Roll gently with rolling pin to seal.
Roll in jelly-roll fashion to make a 14" log. Cut into 24 equal slices. Place, cut side down, on parchment-covered baking sheet. Brush with remaining egg mixture; sprinkle with remaining 1 Tbsp of cheese.
Bake 12 - 14 minutes or until golden brown. Serve warm or at room temperature.