To make this cake, start by preheating your oven to 350 F.
Next, grease an 8x8 round cake pan well with butter or olive oil, or line it with a sheet of parchment paper. Once the pan is prepped, set it aside (note: if you are making a double-layer cake, you'll need to use two pans).
Prepare the cake batter by adding all of the wet ingredients (the olive oil, eggs, pumpkin puree, and vanilla extract) to a large bowl and whisking them until smooth.
Then, in a separate large bowl, add all of the dry ingredients (the gluten-free 1:1 baking flour, baking soda, baking powder, pumpkin pie spice, ground ginger, cinnamon, kosher salt, coconut sugar, and granulated sugar or monk fruit sweetener) and whisk them until they're fully combined.
Pour the wet ingredients into the dry ingredients and gently mix until smooth. Be sure to not over-mix the batter, so that the cake maintains a light and fluffy texture.
Once the batter is mixed, transfer it into your cake pan(s) and use a spatula to spread the batter out evenly.
Then, transfer the cake into the oven and allow it to bake for 35-38 minutes, or until the top is golden and a toothpick comes out clean.
While the cakes are baking, prepare the Spiced Cream Cheese Frosting. Soften the cream cheese, if needed, and add it to the bowl of a stand mixer (or a large mixing bowl), alongside the unsalted butter, powdered sugar, pumpkin pie spice, ground ginger, and vanilla extract. Beat the mixture until it's completely smooth and creamy, then set it aside.
Then, once the cakes are done, remove them from the oven and allow them to cool completely - this is very important!
Once the cakes are completely cool, carefully remove them from the pans. Spread the frosting evenly across the cakes - if you're making a double-layer cake, stack one of the frosted layers on top of the other.
Garnish the cake with chopped unsalted walnuts, if desired. Then, slice, serve, and enjoy!