Preheat the oven to 350 and grease an 8x8 pan with cooking spray.
In a large bowl, whisk together ½ cup granulated sugar, ¼ cup light brown sugar, ¼ cup vegetable oil, 7.5 oz pumpkin puree, 1 large egg and ½ tsp vanilla extract until smooth.
Sprinkle ½ tsp baking powder, ½ tsp baking soda, ¼ tsp kosher salt, 1 tsp cinnamon, ¼ tsp nutmeg, and ¼ tsp ground ginger over the pumpkin mixture and whisk to combine thoroughly. Finally, fold in ¾ cup + 2 tbsp all-purpose flour until fully combined (don't overmix to prevent overdeveloping the gluten--a few lumps are normal and okay!).
Pour the batter into the prepared pan. Place on the middle rack and bake for 20-25 minutes, or until the top springs back under your finger and an inserted tester comes out clean. Let cool in the pan completely before frosting.
Add 4 tbsp unsalted butter and 6 tbsp full-fat cream cheese (can be cold from the fridge) tbsp cream cheese to a stand mixer and mix on medium speed until softened and creamy, about 1 minute.
Add 2 cups powdered sugar and mix on low speed until combined. Add ½ tsp vanilla and a ¼ tsp kosher salt, then whip on medium-high for 2-3 minutes, or until it lightens in color and is very airy. If the consistency looks thicker than you'd prefer, add 1 tbsp cream or milk and whip for another minute until smooth and billowy. Spread frosting evenly on top of the cake, then use an offset spatula to draw lines on the top of the cake to mimic the Trader Joe's cake. Enjoy!
