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Preheat the oven to 350°F. Generously grease a 9-inch springform pan with butter. Cut a circle of parchment paper to fit the bottom of the pan, insert it, and grease it, too.
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Sift together the potato starch and baking powder into a bowl.
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Reserve 2 tablespoons of the sugar. In the bowl of a stand mixer with a paddle attachment, add the remaining sugar. Beat the butter and sugar on medium-high speed until light in color and fluffy, about 5 minutes. Mix in the egg yolks one at a time, scraping down the sides of the bowl in between additions. Beat in the lemon zest and vanilla. Turn the mixer to the stir setting and add the potato starch mixture. Mix only until blended; do not overmix.
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In a separate bowl, whip the egg whites to soft peaks. Whisk in the reserved sugar and continue whisking the egg whites until stiff peaks form and the mixture has a sheen to it. Fold the egg whites into the batter in two batches. Evenly spread the batter into the prepared springform pan. Bake the cake until it has risen, is nicely golden, and is starting to pull from the pan, about 45 minutes. Let cool completely.
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Cut the cake into wedges and top with the balsamic strawberries, a dollop of the crème fraîche, a sprinkle of pepper, and the sprigs of basil.