Preheat oven to 350°F with oven rack in lower third. Butter a 9-by-13-by-2-inch baking pan. Line pan with parchment, leaving a 2-inch overhang on long sides. Whisk together butter, sugar, molasses, and eggs in a bowl.
Sift together flour, baking soda, salt, ginger, cinnamon, cloves, nutmeg, and allspice in a second bowl. Whisk dry ingredients into wet ingredients. Whisk in water until well blended. Fold in candied ginger. Pour into prepared pan.
Bake until a wooden pick inserted into center comes out clean, 45 to 50 minutes. Cool in pan on a wire rack 15 minutes.
Meanwhile, make Chantilly Cream: Whisk together cream, sugar, and vanilla extract or coffee with an electric mixer on medium-high speed until starting to thicken. Reduce speed to medium and beat until cream holds soft, shiny, medium peaks, 2 to 3 minutes; do not overbeat.
Cut cake into 12 to 16 squares. Serve warm topped with Chantilly Cream.
