Preheat oven to 350°F. Use the base of a 6-inch aluminum cake pan (do not use nonstick) to trace a circle on a sheet of parchment paper. Cut out circle and place on the bottom of the cake pan. Cut another sheet of parchment paper 6 inches by 20 inches and nestle into the sides of the cake pan to form a collar. Do not grease the pan or the parchment.
Separate eggs carefully, putting whites in the bowl of a stand mixer and yolks in a large bowl. Whip egg whites with the whisk attachment on medium speed until soft peaks start to form. Add cream of tartar and mix until incorporated. Mix in 1/4 cup sugar, a little bit at a time, until incorporated. Continue whipping until stiff peaks have formed.
To the yolks, add the rest of the sugar and beat vigorously with a whisk until yolks are pale in color and fall in ribbons when the whisk is lifted. Add vegetable oil, vanilla extract, lemon juice, and water, and whisk to combine.
Sift cake flour and salt together 3 to 4 times in a separate bowl, then stir into yolk mixture, a little at a time, until incorporated.
Rewhip egg whites for a few seconds if needed to ensure stiff peaks. Using whisk, add one-third of the whites into the yolk mixture, using few and gentle strokes to incorporate the mixture. Add another third and stir in gently.
Switch to a spatula, and this time take the yolk mixture and add to the remaining one-third of the whites in the mixer bowl. Very gently (so as to not deflate the air incorporated into the whites), fold the batter until just combined and no white streaks remain.
Pour batter into the collared cake pan, stopping if the batter hits the top of the pan. Tap the cake pan on the counter a few times to release any air bubbles.
Bake for 30 to 45 minutes, until tester comes out clean. Cake should be well-browned on top, and the middle should spring back when lightly pressed. Carefully remove cake from the pan and parchment paper, using a knife to loosen the sides if needed. Cool on a wire rack.
While cake is cooling, make the simple syrup: In a small saucepan, bring 1/4 cup water, 1/4 cup granulated sugar, and lemon peel to a near boil, turning the heat off when the water just starts to simmer. Stir to dissolve sugar and place in fridge to cool.
Whip heavy cream in mixer until soft peaks form. Add vanilla and a pinch of salt to incorporate, then keep whipping on medium speed while adding in powdered sugar, a bit at a time, until stiff peaks form.
To assemble cake, trim the top brown pieces off the cake. Cut cake in half horizontally to make two layers. Place one layer on a cake stand, and brush some simple syrup over the top of the cake. Spread a layer of whipped cream, and then arrange strawberry slices to cover. Place second layer of cake, brush simple syrup, and ice your cake fully with whipped cream. Decorate the top of the cake with strawberry slices, and brush a bit more of simple syrup on the fruit. Chill in fridge before serving.
Irene runs a monthly Brooklyn-based pop-up series called Yooeating, with new takes on Korean home cooking, street food, and drinking culture by pairing with other culinary cuisines that feel like home.