In a mixer fitted with the paddle attachment, cream the sugars and butter together. Add the egg and treacle (molasses) and mix until combined.
In a separate bowl, combine the flour, cayenne pepper, white pepper, salt, baking soda, cinnamon, nutmeg and ginger; mix thoroughly. Add the dry mix to the wet batter and mix on medium speed until completely incorporated, about 3 to 5 minutes. Refrigerate dough for at least 2 hours in a metal bowl.
Roll the dough into 20 mm (1 in) logs. Sprinkle the remaining 450 g (2 c) of sugar onto a large plate. Roll the logs in the sugar until completely covered. Refrigerate once more on a baking sheet for at least an hour.
Preheat the oven to 165°C/325°F/Gas 3. Cut the logs into 1 cm (¼ in) thick cookies and bake for 8 to 10 minutes, rotating the sheet 180 degrees after the first 5 minutes.