Preheat oven to 350°F. Lightly coat a 9-inch round cake pan with baking spray; set aside.
Whisk together yogurt, eggs, granulated sugar, oil, orange zest, and vanilla extract in a large bowl until smooth. Add flour, baking powder, and salt; whisk until dry ingredients are just incorporated. Pour batter into prepared cake pan, and smooth top.
Bake in preheated oven until golden brown and a wooden pick inserted into center of cake comes out clean, 35 to 40 minutes. Let cake cool in pan for 10 minutes. Run a knife around the edge of the pan to loosen; invert cake onto a wire rack. Let cake cool completely on rack, 1 to 2 hours.
Dust cake with powdered sugar. Serve slices with berry compote and additional yogurt.
