Place the sliced strawberries into a mixing bowl and stir in 1 cup of sugar. Cover, and refrigerate 2 hours to overnight. Stir the strawberries occasionally. The longer they sit in the syrup, the more syrup you will have.
Preheat an oven to 375 degrees F (190 degrees C). Grease and flour a 9x13-inch baking dish. Whisk the flour together with cornstarch, and baking powder in a mixing bowl.
Beat the egg yolks in a small bowl with the vanilla extract until smooth; set aside. Whip the egg whites with an electric mixer until very stiff. Slowly add the 1 1/4 cup sugar to the egg whites, a few tablespoons at a time, until the sugar is incorporated and the whites are stiff. Fold in the yolk mixture until almost fully blended into the whites. Fold in the flour mixture until just combined. A few small lumps of flour should remain. Scrape the batter into the prepared baking dish.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 22 to 25 minutes. Cool in the pan for 5 minutes, then invert the cake onto a sheet of waxed paper, and cut into 8 equal pieces. While the cake is cooling, whip the heavy cream with the confectioners' sugar to soft peaks.
To assemble the strawberry shortcakes: cut each cake square in half horizontally, and put the bottom halves onto dessert plates. Spoon on the strawberries and syrup, then top with the cake tops. Spoon on whipped cream to serve.