In a medium bowl, mix flour and baking powder.
In a large bowl, combine white sugar, melted butter, and eggs, and beat on medium-high speed using an electric mixer (or whisk vigorously with a metal whisk) for about 2 minutes until the mixture becomes smooth and light in color.
Mix in Greek yogurt and vanilla extract and beat for 1 more minute just until combined.
Add the flour mixture gradually to the wet ingredients, adding about 1 cup at a time and mixing just until combined. Do not over-mix.
Chop up the third (⅓) of halved strawberries into smaller pieces. Fold them into the cake batter.
Add the cake batter to the parchment paper-lined springform pan. It will be thick and lumpy, so spread it out in the pan. (The strawberries will release moisture as they bake to compensate for the thickness of the cake batter.) Spread halved strawberries (cut sides down) densely over the top of the cake (see photos for reference). Add blueberries in spaces between the strawberries.
Place the pan with the cake batter on the middle rack (this is especially important for non-convection ovens). Bake for about 50 or 60 minutes or until the tester (or toothpick) inserted in the center of the cake (away from the strawberries) comes out clean.
Remove the cake from the oven. Let it cool in a springform pan on a wire rack. After the cake has cooled for about 40 minutes, release the cake from the springform pan. At this point, if the cake is cool enough, you can slide your hand (or a large wide spatula) under the cake, between the parchment paper and the bottom of the pan, and transfer the cake with the parchment paper attached to its bottom onto a cake plate.
When serving, dust with powdered sugar, if desired. Serve it as is, or with whipped cream or plain vanilla ice cream.
Notes
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