Place the rack in the center of the oven and preheat the oven to 350°F. Spray an 8-inch cake pan with nonstick or baking spray. Set aside.
Stir together the flour, sugar, baking powder and salt. Add yogurt, oil, eggs, and vanilla extract. Stir to combine. Fold in the chopped peaches. Transfer the batter into the prepared pan.
Slide into the oven until the cake begins to come away from the sides of the pan; it will be golden brown and a knife inserted into the center of the cake will come out clean, 55 to 60 minutes.
Transfer the pan to a rack, cool for 5 minutes, then run a blunt knife between the cake and the sides of the pan. Unmold and cool to room temperature right-side up. Dust with confectioner's sugar. Slice with a serrated knife. Keeps for up to 3 days in an airtight container.