Preheat your oven to 350°F. If you have a convection setting, opt for convection bake. Line the bottom and sides of a 9x3-inch springform pan with a large piece of parchment paper.
In a medium bowl, combine the flour and baking powder.
In a separate large bowl, whisk together granulated sugar, melted butter, and eggs until the mixture becomes light, smooth, and fluffy, about 1 to 2 minutes. Stir in Greek yogurt and vanilla extract until just combined.
Gradually add the flour mixture to the wet ingredients, whisking in one cup at a time until fully combined. Be careful not to over-mix.
In the same bowl used for the flour mixture, gently coat ⅔ of the blackberries with 1 tablespoon of flour. Carefully fold the flour-coated blackberries into the batter.
Transfer the cake batter into the prepared springform pan.
Arrange the remaining ⅓ of the blackberries on top of the cake batter.
Place the springform pan on the middle rack of your oven. Bake for approximately 45 to 50 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Once baked, remove the cake from the oven and allow it to cool in the springform pan on a wire rack for about 20 minutes. After cooling, carefully release the cake from the pan.
Just before serving, dust the cake with powdered sugar.
