Preheat oven to 350 degrees F (175 degrees C). Arrange racks in upper and lower thirds of oven. Line 2 baking sheets with parchment paper.
Whisk together flour, ginger, baking soda, allspice, mustard powder, salt, and pepper in a bowl. Beat together butter, date sugar, and 1/2 cup raw sugar in a separate bowl with an electric mixer at medium speed until light and fluffy, about 3 minutes. Beat in syrup and egg. Reduce mixer speed to low and gradually beat in flour mixture until a soft dough forms. Turn out dough and wrap in plastic wrap; refrigerate 1 hour.
Cut dough into 14 pieces and roll each into a ball between your hands until smooth. Transfer to prepared baking sheets, spacing at least 3 inches apart. Flatten into 2 1/2-inch rounds (about 1/2 inch thick). Sprinkle with remaining tablespoon raw sugar.
Bake, switching positions of sheets halfway through baking, until set, 12 to 15 minutes. Let cool 1 minute on baking sheets, then transfer to a wire rack to cool completely, about 20 minutes.