Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a large mixing bowl, whisk together the Greek yogurt, granulated sugar, and eggs until smooth and well combined.
Add the vegetable oil and vanilla extract to the yogurt mixture and 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 half of the batter into the prepared cake pan.
Arrange half of the kiwi slices evenly over the batter in the pan.
Pour the remaining batter over the kiwi slices and spread evenly.
Top the cake with the remaining kiwi slices, pressing them lightly into the batter.
Bake in the preheated oven 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.
Transfer the cake to a wire rack to cool completely.
Once cooled, dust the top with powdered sugar if desired before serving.