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 whisk or electric mixer until pale and slightly thickened, about 2 minutes.
Slowly drizzle in the olive oil while continuing to whisk until fully incorporated.
Add the fresh orange juice, orange zest, Greek yogurt, and vanilla extract to the wet ingredients and mix until smooth.
Gradually fold the dry ingredients into the wet ingredients using a spatula until just combined, being careful not to overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 40 to 45 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 to loosen the cake, then turn it out onto a wire rack to cool completely before serving.