Heat oven to 350 degrees. Grease a 9-inch round cake pan with butter or cooking spray. Line with parchment and grease parchment. Or use mini paper cake pans that you have coated in cooking spray.
Cut off tops of strawberries and thinly slice half of them, leaving remaining berries whole. Mix sliced strawberries with superfine sugar and half the lemon zest and 2 teaspoons of lemon juice. Set aside.
In a small bowl, whisk together flour, baking powder and salt. In the bowl of an electric mixer fitted with the whisk attachment, whip eggs and egg white on high speed until frothy, about 30 seconds. Gradually pour in 1 1/4 cups sugar. Whip on high speed until mixture is a pale yellow and thick, 1 to 3 minutes.
Fold flour mixture into egg mixture. Fold in milk, vanilla and butter until completely combined. (I melt the butter in the milk when warming in the microwave for 30 to 45 seconds).
Gently pour batter into prepared pan and bake until golden brown, 30 to 35 minutes. Let cool 10 minutes in pan. Invert cake onto a cooling rack and peel off baking paper. Let cool completely. If you are using mini cake pans, bake for 15 minutes, then check, and turn to evenly distribute heat. Check again after 5 minutes.
To make syrup: In a small saucepan, whisk together 1/2 cup) sugar, 3 tablespoons plus 1 teaspoon water, 2 teaspoons lemon juice, and optional pepper. Simmer on medium heat until sugar is dissolved and mixture has reduced by half, about 5 minutes. Remove from heat and stir in remaining lemon zest.
Whip heavy cream and vanilla until soft peaks form.
Using a serrated knife, horizontally slice cake in half. Generously brush each cut side with lemon syrup. Place the bottom half, cut side up, on a cake plate. Spoon sliced strawberries and any juices over it. Spread half the whipped cream over strawberries. Place the other cake half on top. Spread remaining whipped cream on top. Garnish with whole strawberries and drizzle with more lemon syrup for serving.