To make the Bars
Preheat the oven to 350°F. Line a 8 by 8-inch baking pan with foil or parchment paper, leaving an overhang. Spray with non-stick cooking spray.
In a medium bowl combine the flour, cinnamon, ginger, nutmeg, baking soda and salt.
In a large bowl whisk together the melted butter, brown sugar, egg, vanilla, and pumpkin. Add the butter mixture to the flour mixture, stirring until just combined. Pour the batter into the prepared pan.
Bake for 25 minutes, or until a cake tester inserted into the center comes out clean. Be careful not to overbake. Set the pan on a wire rack to cool completely.
To make the Frosting
In a large bowl, use an electric mixer to beat the butter, brown sugar, and maple syrup on medium-high speed until light, fluffy, and smooth. Add the cinnamon and salt and mix in. On low speed gradually add in the powered sugar until incorporated.
Add the vanilla and milk and increase the speed to medium-high. Beat until very light and fluffy. If too runny, add more powered sugar, If too thick, add more milk. Spread evenly all over the pumpkin bars.
Top the bars with the chopped walnuts and cut them into squares.