Preheat the oven to 350°F and prepare a 9-inch cake pan by spraying it and lining the bottom with parchment paper. Spray the parchment as well—this cake tends to be a little sticky!
In a small bowl, whisk together the flour, baking powder, and baking soda.
In a larger bowl, add the softened butter, sugar, and eggs, and beat with a mixer until light and fluffy. Add the vanilla, Greek yogurt, and milk, and mix for another minute until the batter is creamy and pale in color.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix!
Pour the batter into the prepared cake pan. Scatter half of the sliced peaches and half of the blueberries evenly over the surface; they will naturally sink into the batter as it bakes.
Bake for about 60 minutes. Halfway through, once the top is set and the fruit has begun to sink, carefully remove the cake from the oven and arrange the remaining fruit on top in a decorative pattern. Return the cake to the oven for the remaining time. The cake is done when a toothpick inserted into the center comes out clean.
Let the cake cool in the pan on a wire rack for 45 minutes to an hour.
Before serving, dust with powdered sugar or drizzle with honey, as desired. The cake will keep in the refrigerator for up to three days, though it’s best enjoyed fresh—over time, the fruit may make it a bit soggy.