Preheat oven to 175°C (350°F). Grease and line a 9-inch springform pan with parchment paper.
In a bowl, sift together flour, baking powder, and baking soda.
In another bowl, beat butter, sugar, and eggs until light and fluffy (2–3 minutes).
Add vanilla and Greek yogurt, and mix until smooth and creamy.
Gradually mix in the dry ingredients on low speed until just combined. Do not overmix.
Pour the batter into the prepared pan.
Arrange peach slices on top and scatter blueberries evenly.
Sprinkle fruit with a teaspoon of sugar.
Bake for about 1 hour, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 40 minutes, then remove and transfer to a serving plate.
This peach blueberry Greek yogurt cake is best enjoyed slightly warm or at room temperature.