Preheat your oven to 350°F (175°C). Grease an 8-inch or 9-inch round cake pan with a little olive oil and line the bottom with parchment paper to ensure easy removal after baking.
In a medium mixing bowl, whisk together the all-purpose flour, granulated sugar, brown sugar, baking soda, baking powder, salt, and pumpkin pie spice until well combined and free of large lumps.
In a separate large bowl, combine the pumpkin puree, extra virgin olive oil, eggs, and vanilla extract. Whisk vigorously until the mixture is smooth and the eggs are fully incorporated.
Gently fold the dry ingredients into the wet ingredients using a spatula. Mix until just combined and no streaks of flour remain. Be careful not to overmix, as this can lead to a dense cake.
Pour the batter into the prepared cake pan and smooth the top. Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs attached.
Let the cake cool in the pan for about 10 minutes before transferring it to a wire rack. Allow it to cool completely before slicing or adding any toppings.