Preheat the oven to 350 degrees Fahrenheit and grease a 6-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, ground ginger, and salt.
In a separate bowl, mix the pumpkin puree, brown sugar, vegetable oil, egg, and vanilla extract until smooth.
Combine the wet and dry ingredients and stir until just blended. Pour the batter into the prepared pan and smooth the top.
Bake for 25 to 28 minutes until a toothpick inserted in the center comes out clean. Let the cake cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.
For the buttercream, beat the softened butter with an electric mixer until creamy. Gradually add the powdered sugar and continue beating until light. Mix in the melted white chocolate until fully incorporated. Stir in the chopped candied ginger by hand.
Spread the buttercream evenly over the cooled cake.