Preheat the Oven: Set your oven to 350°F and grease a 9-inch springform pan.
Cream Butter and Sugar: Using a stand mixer with a paddle attachment or a hand mixer, beat the softened butter and sugar together until the mixture is light and fluffy.
Incorporate Egg Yolks: One at a time, add the egg yolks, mixing thoroughly after each addition. Stir in the lemon zest and rum.
Mix Dry Ingredients: Gradually add the cornstarch, a couple of tablespoons at a time, while continuing to mix. Slowly incorporate the flour, baking powder, and salt. Beat for at least five minutes until well combined.
Whip Egg Whites: In a separate clean bowl, whip the reserved egg whites until stiff peaks form.
Fold in Egg Whites: Gently fold the whipped egg whites into the batter in three separate additions. Be careful to maintain the airy texture and mix until no streaks remain.
Bake: Pour the batter into the prepared pan and bake for 45 to 50 minutes, or until a toothpick inserted in the center comes out with only a few small crumbs. The cake should begin to pull away from the pan's edges when done.
Cool: Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely for about an hour.
Decorate: Once cooled, place a doily over the cake and dust it generously with powdered sugar. Carefully remove the doily to reveal a beautiful lace pattern.