Begin by heating your oven to 350°F, 175°C. Lightly grease a 6-inch round cake pan, then line the base with parchment paper for easy removal after baking.
Place ¾ cup of the strawberries, the water, and 1 tablespoon of the sugar into a small saucepan. Cook over medium heat, stirring from time to time, until the mixture comes to a gentle boil. Let it simmer for 4 to 5 minutes, or until the berries soften and thicken into a jam-like consistency. You should end up with about 2 generous tablespoons of strawberry mixture. Set aside to cool for about 15 minutes.
In a bowl, sift together the flour and cornstarch, then whisk in the baking powder and salt until evenly combined.
Using a stand mixer fitted with the paddle attachment, or a hand mixer, beat the butter and the remaining ½ cup sugar on medium-high speed until smooth and creamy, about 1 minute.
Scrape down the sides of the bowl. Add the egg whites one at a time, mixing well after each addition. Stir in the vanilla extract until the mixture is smooth. There is no need to whip the egg whites separately, simply incorporate them as you would whole eggs.
Reduce the mixer speed to low. Add the dry ingredients and milk alternately, beginning and ending with the flour mixture. Add the flour in three portions and the milk in two portions, mixing gently after each addition.
For the final portion of flour, put away the mixer and use a rubber spatula to fold it in by hand. This keeps the batter light and tender, so avoid excessive mixing.
Gently fold in the cooled strawberry mixture along with the remaining ¼ cup of fresh strawberries. If desired, add a few drops of food coloring until the batter reaches a soft pink shade. Keep in mind that the color will become slightly lighter during baking.
Pour the batter into the prepared cake pan and smooth the top. Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to rest in the pan for 15 minutes before carefully turning it out onto a wire rack. Let it cool completely before frosting.
Once cooled, decorate with your favorite frosting. If using buttercream, the cake can be stored covered at room temperature for up to 2 days. For cream cheese frosting or longer storage, keep it refrigerated for up to 1 week.
For the best flavor and texture, allow the chilled cake to sit at room temperature for about 30 minutes before serving.