Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger. Set aside.
In a large mixing bowl, combine the pumpkin puree, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract. Mix until well blended.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
In another bowl, beat together the cream cheese, powdered sugar, egg, and vanilla extract until smooth.
Pour half of the pumpkin batter into the prepared baking pan. Spread the cream cheese mixture over the pumpkin batter. Pour the remaining pumpkin batter on top and spread gently.
In a small bowl, combine the flour, brown sugar, and cinnamon for the crumb topping. Pour in the melted butter and mix until crumbly. Sprinkle the crumb topping over the cake.
Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Allow to cool in the pan before slicing and serving. Enjoy!