1. Whisk together flour, both gingers, baking powder, and salt in a bowl. Beat butter with sugar on medium-high speed until pale and fluffy, about 3 minutes. Beat in egg and vanilla. Reduce speed to low; gradually beat in flour mixture until combined.

2. Divide dough in half. Knead molasses into one portion, honey into other. On a lightly floured surface, knead each piece and form into balls. Wrap each in plastic and refrigerate until firm but still pliable, about 30 minutes. (Dough can be refrigerated up to 3 days; let stand at room temperature until pliable, 10 minutes.)

3. Preheat oven to 325 degrees. Divide each dough ball into about 3 dozen 1-inch balls (about 2 teaspoons each). On a lightly floured surface, shape into ropes, each about 9 inches long. (If ropes crack or break, simply press dough back together.) Twist pairs of opposite-colored ropes together, gently stretching each pair into a 12-inch spiral strand. Cut each strand in half crosswise; form each piece into a candy-cane or pretzel shape. (Or roll out dough and cut out shapes with cookie cutters.) Transfer to parchment-lined baking sheets, 1 1/2 inches apart. Freeze until firm, about 30 minutes.

4. Bake, rotating sheets halfway through, until cookies are golden on edges, 14 to 16 minutes. Let cool completely on sheets on wire racks. Cookies can be stored in an airtight container up to 1 week.