Preheat the oven to 350°F (175°C). Grease and flour a 9-inch (23 cm) round cake pan.
In a large mixing bowl, whisk together the yogurt, granulated sugar, and eggs until smooth and well combined.
Add the vegetable oil, orange zest, fresh orange juice, and vanilla extract to the yogurt mixture. Whisk until fully incorporated.
In a separate bowl, sift together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35 to 40 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Turn the cake out onto a wire rack to cool completely.
Once cooled, dust the top with powdered sugar if desired before serving.