Preheat the oven to 350 degrees F. Butter a 9-inch round cake pan and dust it with 1 tablespoon of the sugar.
In a medium bowl, combine the cheese with the 3/4 cup sugar, lemon juice, lemon zest, and vanilla. Beat at medium speed until smooth. Beat in the egg yolks, one at a time, incorporating each one completely before adding the next. Turn the mixer to low and add the flour.
In another bowl, using clean beater, beat the egg whites until firm. Beat one third of the egg whites into the cheese mixture. Gently fold in the rest of the egg whites. Spoon the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean and the cake is a deep golden brown, 35 to 40 minutes. Do not underbake or you'll have an eggy mess. Cool for 15 minutes on a cooling rack. Remove the cake from the pan and cool completely.
In a bowl, mix the peaches and blueberries together with the remaining 1 tablespoon sugar. (You may need less or more sugar, depending on the sweetness of the fruit.) Set aside.
When ready to serve, invert the cake onto a serving plate. Dust with confectioners' sugar, and spoon the fruit on top of the cake, leaving a 1-inch border all the way around. Cut and serve, garnishing each piece with a little whipped cream, if desired.