Preheat the oven to 350 degrees F. Grease a 9x13-inch baking dish with nonstick spray.
In a large bowl, whisk together the flour, baking powder, salt, cinnamon, ginger, and nutmeg. Set aside.
In the bowl of an electric mixer, beat together the butter and pumpkin puree until combined. Add the sugar and beat until well combined. Beat in the eggs and vanilla.
Add the flour mixture to the mixing bowl in three additions, alternating with the milk. Continue to mix on low speed until just combined.