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Preheat your oven to 350°F.
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In a medium bowl, combine the flour and baking powder.
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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.
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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.
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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.
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Transfer the cake batter into the prepared springform pan.
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Arrange the remaining ⅓ of the blackberries on top of the cake batter.
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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. I baked this cake using a convection bake setting for 45 minutes at 350°F. If needed, bake for an additional 5 to 15 minutes, checking every 5 minutes.
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Once baked, remove the cake from the oven and allow it to cool in the springform pan for about 15-20 minutes. After cooling, carefully release the cake from the pan.
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Once the cake has cooled, dust the cake with powdered sugar.
