Preheat oven to 325°. Butter two 8- by 8-in. glass or light-colored metal baking dishes. Bring Guinness stout and dark molasses to a boil in a large, deep saucepan. Remove from heat and whisk in baking soda (it will foam up dramatically); let cool. In a bowl, whisk together cinnamon, ginger, allspice, salt, and flour.
In a large bowl, combine 1 cup crystallized ginger, melted butter, and dark brown sugar and stir together with a wooden spoon. Add eggs and lemon zest and stir once more. Gradually stir in dry ingredients in four batches, alternating with Guinness mixture. Pour batter into greased baking dishes, dividing evenly.
Bake 30 to 40 minutes, or until a toothpick inserted into centers comes out clean. Cool cakes on a wire rack, then dust tops with powdered sugar. Cut each cake into 4 to 6 squares and arrange on a serving platter.
In a small bowl, whip cream and granulated sugar together until cream holds soft peaks. Stir in all but a teaspoon of crystallized ginger and serve in a bowl alongside the cake, sprinkled with the last bit of ginger.
Note: Nutritional analysis is per serving.
May be made up to 2 days ahead. Cool, cover with plastic wrap, and store at room temperature.