Prep: Preheat your oven to 180°C. Grease a 9-inch springform pan generously with butter, rubbing it in by hand across the base and sides. Flour or parchment paper isn't strictly necessary for this cake, but if your pan isn't the best quality, feel free to add both for extra insurance.
Dry mix: In a bowl, whisk together the flour, salt, and baking powder. Set aside.
Cream butter and sugar: In a separate large bowl or the bowl of a stand mixer, beat the butter alone for about 30 seconds until creamy. Add the sugar and beat on medium-high for about 3 minutes, until pale and fluffy.
Add eggs: Add the eggs one at a time, mixing well after each addition until fully incorporated.
Add yogurt and vanilla: Mix in the yogurt (or sour cream) and vanilla extract until smooth.
Fold in flour: With the mixer on low, add the dry mix gradually, stopping just before it's fully combined. Finish folding by hand with a spatula to avoid overmixing.
Prep the peaches: Slice your peaches thinly, aiming for about 2 cups total. Gently fold three-quarters of the peaches into the batter, reserving the prettiest slices for the top.
Assemble: Pour the batter into the prepared pan and smooth the top. Arrange the reserved peach slices on top — in a pattern, or scattered naturally, both look beautiful. Sprinkle the sugar over the top.
Bake: Bake at 180°C for 45 minutes if your oven uses both heating rods, or closer to 55 minutes if you're baking on the middle rack with only the bottom rod. The cake is done when a skewer inserted in the centre comes out clean.
Cool and serve: Let the cake cool completely in the pan before releasing the springform sides. Dust generously with powdered sugar just before serving.