Preheat the oven to 350° F. Grease and flour two 9-inch round spring-form pans or cake pans. Cut a round of parchment paper to fit into the bottom of the pan. Grease and flour the parchment paper.
In a large bowl, whisk together the flour, cornstarch, baking powder and salt. Set aside.
In the bowl of a large stand mixer, beat the softened butter with the 1 ½ cups of granulated sugar for about 5 minutes: the mixture should be fluffy and pale yellow in color. With the mixer running on low, slowly pour in the egg whites and vanilla, and mix them into the butter-sugar mixture.
Add to the mixing bowl a third of the flour mixture and run the mixer until it is just combined. Add in half of the milk and mix this in too. Repeat these steps with another third of the flour mixture, then the rest of the milk and then finally the last of the flour mixture. The batter should be smooth.
Divide the batter evenly between the two prepared cake pans. Bake the cakes for 30 minutes.
While the cakes bake, prepare the lemon syrup: to a small saucepan add the ½ cup of granulated sugar and the lemon juice. Stir these together and heat the mixture over medium heat. Stir occasionally while you bring it to a boil. Once it's boiling, reduce the heat slightly and simmer for 5 minutes, stirring it occasionally. After 5 minutes, remove the pan from the heat. Allow it to sit and cool slightly while the cakes finish baking.
After the cakes have baked for 30 minutes, check them by inserting a toothpick or wooden skewer into the center - it should come out clean. If necessary, bake the cakes a few minutes longer until the tester comes out clean.
Remove the pans from the oven and place them on a cooling rack. Use a pastry or silicone brush to brush the tops of the hot cakes with the lemon syrup. Stop when the tops of the cakes seem moistened - you will not need all of the syrup. The remaining syrup can be poured into a jar and refrigerated for up to two weeks (or you can discard it.)
Allow the cakes to cool completely. Remove the cakes from the pans and peel off the parchment rounds. Wrap the cakes in plastic wrap and refrigerate the layers for at least 1 hour or up to two days.