Position a rack in the center of the oven and preheat to 325 degrees F. Line an 8-inch square metal baking pan with a 12-by-8-inch piece of parchment paper leaving an overhang on 2 sides.
Melt the butter in a small microwave-safe bowl in the microwave, about 1 minute. Brush the parchment paper with some of the melted butter, then flip it over and press it back in the pan. Brush the other side of the paper and the sides of the pan with butter.
Whisk the egg yolks and sugar vigorously in a large bowl until pale, creamy and thick, 1 to 2 minutes. Pour in the remaining melted butter and whisk until incorporated. Add the salt and all but 2 tablespoons of the flour, mixing until completely combined.
Heat the milk in a microwave safe bowl or measuring cup in the microwave until warm, about 1 minute. Slowly add the milk and vanilla to the egg yolk mixture, whisking constantly until well combined (the batter will be thin). Toss the berries with the reserved 2 tablespoons flour and gently stir into the mixture.
Beat the egg whites and the cream of tartar in a clean bowl with an electric mixer on medium speed in until stiff peaks form, about 2 minutes. Scrape the whites into the yolk mixture, gently breaking them up a little with a whisk. Using a whisk, gently stir and fold the mixture a few times to coat the whites with liquid while keeping as much volume as possible (the batter will not be homogeneous). Pour the batter into the prepared pan and gently smooth the top with a rubber spatula.
Bake until the top is browned and puffed and the cake is mostly set with a slight jiggle in the center, about 1 hour. Let the cake cool completely in the pan, about 2 hours.
To serve, dust the top of the cake with confectioners' sugar. Run a small offset spatula or thin knife around the edges of the pan to loosen. Use the parchment paper overhang to lift the cake from the pan and place it on a cutting board. Cut the cake into 9 squares and serve topped with whipped cream.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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