Beat butter and sugar at high speed until fluffy (about 5 minutes).

Mix in ginger, cinnamon, allspice, baking soda, and cloves at low speed until blended.

Beat in the egg.

Add 2 cups of flour and mix at low speed until just combined.

Beat in molasses until just blended.

Add remaining 2 cups of flour and mix at low speed until just combined.

Divide dough into thirds, form into disks, and wrap in plastic wrap or waxed paper.

Chill until firm (at least 1 hour or up to 2 days).

Arrange racks in the upper and lower thirds of the oven and preheat to 375°F.

Line baking sheets with parchment paper.

Remove 1 dough disk from the refrigerator.

On a lightly floured surface, roll out dough to 1/4- to 1/8-inch thickness.

Use a 3- to 4-inch candy cane cookie cutter to cut out cookies.

Transfer cookies to baking sheets with a spatula.

Gather and reroll scraps and cut out additional cookies.

Decorate with stripes of red and green sanding sugar.

Chill cookies for 10 minutes.

Bake until fragrant and lightly colored (about 10 minutes).

Cool on pans for 2 minutes.

Transfer to racks and cool completely.

Repeat with remaining dough.