Preheat your oven to 350°F (180°C). This ensures that your cake bakes evenly. While the oven is warming, prepare your baking pan by spraying an 8-inch square baking pan with baking spray that contains flour. This will help prevent the cake from sticking.
Line the bottom of the pan with parchment paper. This step is crucial for easy removal of the cake later on. Make sure to press it down well so it adheres.
In the bowl of a stand mixer fitted with the whisk attachment, combine granulated sugar, lemon zest, and thyme. Beat at low speed until fragrant, which should take approximately 1 to 2 minutes. This step releases the oils from the herbs and zest, creating a beautiful aroma.
Add the eggs to the mixture and increase the speed to medium-high. Beat until your mixture becomes thick and pale, about 5 to 7 minutes. You want to incorporate as much air as possible for a light cake.
With the mixer on medium-low speed, gradually pour in the olive oil and vanilla extract. Beat until everything is well combined. The mixture should become glossy and smooth.
Add the Greek yogurt and continue to beat until it's fully incorporated. This will add moisture and tenderness to the cake.
In a separate medium bowl, whisk together all-purpose flour, baking powder, and kosher salt. This will help evenly distribute the leavening agent.
With the mixer on low speed, gradually add the flour mixture to the sugar mixture. Beat until just combined, taking care not to overmix. Stop to scrape the bottom and sides of the bowl periodically to ensure everything is well blended.
Pour the batter into the prepared baking pan and spread it out evenly. A spatula works well for this step.
Bake in the preheated oven for 30 to 35 minutes, or until a wooden pick inserted in the center comes out clean. This is a crucial step, as you want to avoid underbaking.
Once baked, let the cake cool in the pan for about 5 minutes. Then, carefully remove it from the pan and let it cool completely on a wire rack. This allows air to circulate around the cake, keeping it from becoming soggy.
Just before serving, brush the top with a little extra olive oil for added flavor and shine. Garnish with lemon slices for a beautiful presentation.
Store any leftovers in an airtight container for up to 3 days. This cake stays delicious for a while!
