Preheat the oven to 350°F and coat an 8" cake pan with cake goop or parchment paper. You can also use a springform pan or loaf pan if you prefer, just adjust the baking time. Mix the eggs and granulated sugar in a bowl of a stand mixer with the whisk attachment on medium speed and mix until it's light in color and fluffy.
Slowly drizzle the olive oil in between the whisk blades and the side of the bowl and mix until combined.
Switch to the paddle attachment and add the water, lemon extract, vanilla extract, and lemon zest, then mix until combined.
Add the flour, buttermilk powder, baking soda, and salt to a large bowl and whisk it to combine.
Pour the dry ingredients into the wet ingredients while mixing on low, and mix until combined.
Pour the cake batter into the prepared pan and spread out the top with a spatula.
Bake the cake for 45 to 50 minutes until it's golden brown and a toothpick comes out of the center clean.
Cool the cake in the pan for 10 minutes, then flip it out onto a wire rack to cool completely. If you're making it ahead, wrap it in plastic wrap and freeze it until you're ready to serve.
Place the cake on a serving plate and dust the top of the cake with powdered sugar. I put a little paper heart in the center to make this fun pattern. You can also top it with fresh lemons, lemon curd, or fresh berries.
Store it in an airtight container at room temperature for up to five days. You can refrigerate it if you'd like, but this cake tastes best at room temperature.