Preheat oven to 350 degrees F. Coat a 9-inch round cake pan with cooking spray. Add breadcrumbs, tilting the pan to evenly coat the inside. Tap out the excess.
Combine milk and oil in a measuring cup. Sift flour, baking powder and salt into a bowl; set aside.
Combine eggs, egg yolk, sugar and lemon juice in a mixing bowl. Beat with an electric mixer on high speed until the mixture is thick and pale and falls in a ribbon when the beaters are lifted, about 5 minutes. Beat in lemon zest and vanilla.
Sift half of the reserved dry ingredients over the beaten egg mixture and fold in with a rubber spatula until blended. Fold in half of the milk mixture. Repeat these steps with the remaining dry ingredients and milk mixture.
Pour the batter into the prepared pan. Bake until a skewer inserted in the center comes out clean, 20 to 25 minutes. Let the cake cool in the pan on a wire rack for 5 minutes, then turn out of the pan and place right-side up on the rack to cool completely.
Meanwhile, make Blackberry Sauce.
Dust the cake with confectioners' sugar, slice and serve with the Blackberry Sauce alongside.
Fresh Blackberry Sauce
4 other carbohydrates, 1 fat