Preheat oven to 350°F (180°C). In large bowl, beat butter with sugar until fluffy. Beat in egg and molasses. In medium bowl, whisk flour with ginger, baking soda, cinnamon, cloves, pepper and salt.
Gradually beat flour mixture into butter mixture, until just combined. If necessary use hands to blend together.
Divide dough in half and wrap in plastic wrap. Chill dough 1 hr. On lightly floured surface, or between sheets of waxed paper, roll half the dough to 1/8-in. (1-mm) thickness. With floured 2-in. (5-cm) cookie-cutter, cut out cookies. Re-roll dough as needed. Arrange on parchment paper lined-baking sheets, 2 in. (5 cm) apart. Repeat with remaining dough.
Bake 12 min. or until cookies are firm and bottom is lightly browned, rotating half-way through baking for even cooking. Cool on baking sheets 5 min. Transfer to wire rack to cool completely. Store in airtight container up 1 week or freeze up to 1 month.
If dough becomes soft or slightly sticky, re-wrap in plastic wrap and freeze 10 to 15 min. To help cookies retain shape while baking, freeze cut cookies on cookie sheet 10 to15 min.