One more surprising discovery about acrylamide that I neglected to include in my recent roundup. Among the foods with the highest known acrylamide levels is gingerbread as it's traditionally made in northern Europe--so high that in Holland, gingerbread consumption alone accounts for something like a sixth of the total year-round acrylamide intake. This is despite the fact that wheat flours don't contain nearly as much asparagine as potatoes.
The problem with ammonium carbonate is the ammonia that it releases during baking. It reacts with glucose and fructose in the dough to form unusual molecules that in turn react very efficiently with asparagine to form acrylamide. The Swiss gingerbread dough is made with glucose, fructose, and honey; molasses also contains a lot of glucose and fructose. Ordinary table sugar, sucrose, is not vulnerable to attack by ammonia.
So it's easy to make low-acrylamide gingerbread: either use a standard sodium bicarbonate leavener, or use table sugar for the sweetener, or both.
Amrein, T.M. et al. Acrylamide in gingerbread: critical factors for formation and possible ways for reduction. J. Agric. Food Chem. 2004, 52, 4282-88.
Amrein, T.M. et al. Investigations on the promoting effect of ammonium hydrogencarbonate on the formation of acrylamide in model systems. J. Agric. Food Chem. 2006, 54, 10253-61.