Preheat oven to 350F. Grease a 9”-x-13” baking pan with cooking spray.
In a medium bowl, whisk together flour, cinnamon, salt, baking powder, baking soda, nutmeg, and ginger.
In a large bowl using a hand mixer (or in the bowl of a stand mixer), beat butter and sugars together until light and fluffy. Add eggs, one at a time, beating well after each addition. Add vanilla and pumpkin puree, and beat until incorporated. Add dry ingredients and mix until just combined.
Pour batter into prepared baking pan and smooth top. Bake until a toothpick inserted in middle comes out clean, 30-45 minutes. Let cool completely.
Meanwhile, make frosting: In a large bowl using a hand mixer (or in the bowl of a stand mixer), beat cream cheese and butter until smooth. Add powdered sugar and beat until no lumps remain, then add vanilla and a pinch of salt.
Frost cake using a spatula and top with crushed gingersnaps.