Heat oven to 350 degrees. Using a pastry brush, butter the interiors of six mini Bundt pans. Set aside.
Place fresh ginger and 3/4 cup hot water in small saucepan; bring to a boil. Reduce heat to low; simmer until reduced to 1/2 cup, 10 to 15 minutes. Remove from heat; strain into a bowl; discard ginger. Add molasses and baking soda to liquid. Set aside.
Sift together flour, salt, ground ginger, cinnamon, ground cloves, and baking powder. Set the mixture aside.
In an electric mixer fitted with the paddle attachment and set on medium-high speed, beat remaining 4 tablespoons butter and brown sugar together until light and creamy, about 5 minutes. Add egg, and beat until fluffy, about 5 minutes. Reduce to low speed, and add pumpkin purÃ©e, mixing until just incorporated. Alternately add one quarter of dry ingredients and one third of molasses mixture, ending with dry ingredients. Mix on low speed, scraping bowl after each addition, until incorporated. Transfer mixture to Bundt pans, filling halfway. Bake, uncovered, until golden brown and firm to the touch, about 20 minutes.
Invert Bundt pans onto a sheet pan; tap firmly several times on hard back surface of Bundt pans to release cakes.
Serve the pumpkin pudding cakes with whipped cream and garnish with candied ginger and fresh mint, if desired.