Start to finish: 2 1/2 hours
1 cup (7 ounces) sugar
1 1/4 cups (5 ounces) cake flour
1 1/2 teaspoons baking powder
1/4 teaspoon salt
5 large eggs (2 whole, 3 separated), room temperature
6 tablespoons unsalted butter, melted and cooled
2 tablespoons water
2 teaspoons vanilla extract
Pinch cream of tartar
2 pounds strawberries, hulled (6 cups)
4-6 tablespoons sugar
2 tablespoons kirsch
8 ounces cream cheese, softened
1/2 cup (3 1/2 ounces) sugar
1 teaspoon vanilla extract
1/8 teaspoon salt
2 cups heavy cream, chilled
DIRECTIONS: Adjust oven rack to lower-middle position and heat oven to 325 F. Grease 9-inch round cake pan or 9-inch springform pan, line with parchment paper, grease parchment, and flour pan. Reserve 3 tablespoons sugar in small bowl. Whisk flour, baking powder, salt, and remaining sugar together in bowl. Whisk in 2 eggs and 3 yolks, melted butter, water, and vanilla until smooth.
Using stand mixer fitted with whisk attachment, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip whites to soft billowy mounds, about 1 minute. Gradually add reserved 3 tablespoons sugar and whip until glossy, soft peaks form, 1 to 2 minutes. Using rubber spatula, stir one-third of whites into batter. Gently fold remaining whites into batter until no white streaks remain.
Transfer batter to prepared pan and smooth top with rubber spatula. Bake until toothpick inserted in center comes out clean, 30 to 40 minutes. Let cake cool in pan on wire rack for 10 minutes. Remove cake from pan, discarding parchment, and let cool completely on rack, about 2 hours.
Halve 24 of best-looking berries and reserve. Quarter remaining berries, toss with sugar in bowl, and let sit for 1 hour, stirring occasionally. Drain berries in fine-mesh strainer set over bowl and reserve juice (you should have about 1/2 cup). Pulse macerated berries in food processor until coarsely chopped, about 5 pulses (you should have about 1 1/2 cups). Simmer kirsch and reserved juice in small saucepan over medium-high heat until syrupy and reduced to about 3 tablespoons, 3 to 5 minutes. Add reduced syrup and salt to macerated berries and toss to combine. Set aside.
When cake has cooled, fit stand mixer with whisk attachment and whip cream cheese, sugar, vanilla, and salt on medium-high speed until light and fluffy, 1 to 2 minutes, scraping down bowl as needed. Reduce speed to low and add cream in slow, steady stream; when almost fully combined, increase speed to medium-high and whip until stiff peaks form, 2 to 2 1/2 minutes, scraping down bowl as needed (you should have about 4 1/2 cups).
Using long serrated knife, cut two horizontal lines around sides of cake; then, following scored lines, cut cake into 3 even layers.
Place bottom cake layer on platter. Arrange 20 strawberry halves, cut sides down and stem ends facing out, in ring around perimeter of cake layer. Pour half of pureed berry mixture (about 3/4 cup) in center, then spread evenly to cover cake. Gently spread one-third of whipped cream (about 1 1/2 cups) evenly over berry layer, leaving 1/2-inch border around edge. Top with middle cake layer, pressing lightly to adhere (whipped cream layer should become flush with cake edge). Repeat with 20 strawberry halves, remaining berry mixture, and half of remaining whipped cream. Top with remaining cake layer, pressing lightly to adhere. Spread remaining whipped cream evenly over top and decorate with remaining strawberry halves. Serve. (Cake can be refrigerated for up to 4 hours.)