Preheat the oven to 350°F (180°C). Grease two 6-inch round cake pans. Line the pans with parchment paper. Grease the parchment. Dust the pans with flour.
Combine 1½ cups strawberries (210g) and the water in a small saucepan. Bring to a boil over medium-high heat, and boil 5 minutes, until beginning to thicken. Let cool 15 minutes.
Whisk together the flour, cornstarch, baking powder, and salt in a medium bowl.
Place the butter in a mixing bowl, and using an electric mixer at medium-high speed, beat until creamy. Add the sugar and beat until fluffy, about 5 minutes. Add the egg whites one at a time, and beat until well combined. Reduce the speed to low, and add the flour mixture and milk a little at a time, beginning and ending with the flour mixture. Beat until just smooth. Add the vanilla, and beat 30 seconds. Fold in the cooked strawberries and the ¼ cup sliced strawberries. The batter will be thin. Scrape into the prepared pans.
Bake the cakes 35 to 40 minutes, until a tester inserted into the center comes out almost clean. Place the pans on a wire rack, and let the cakes cool 10 minutes. Remove the cakes from the pans, and return them, top side up, to the rack to cool completely.
Place one layer on a plate or cake stand. Frost the top with about one-third of the Cream Cheese Frosting. Place the second layer on top, and frost the top and sides of the cake. Decorate the sides of the cake with the small sliced strawberries, if using.