Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the eggs and granulated sugar together with a hand mixer or whisk until pale and slightly thickened, about 2-3 minutes.
Gradually add the olive oil in a slow stream while continuing to beat the eggs and sugar mixture.
Add the orange juice, orange zest, and vanilla extract to the wet ingredients and mix until combined.
Add half of the dry ingredients to the wet ingredients and gently fold in using a spatula.
Add the Greek yogurt and fold it in until just combined.
Add the remaining dry ingredients and fold gently until the batter is smooth and uniform, being careful not to overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 38-42 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes.
Run a knife around the edges and invert the cake onto a wire rack to cool completely before serving.