FOR THE CAKE:.
Adjust oven rack to lower-middle position and heat oven to 325 degrees.
Grease and flour round 9 by 2-inch cake pan (pan must be at least 2" high!) or 9-inch springform pan and line with parchment paper.
Whisk flour, baking powder, salt, and all but 3 tablespoons sugar in mixing bowl.
Whisk in 2 whole eggs and 3 yolks (reserving whites), butter, water, and vanilla; whisk until smooth.
In clean bowl of standing mixer fitted with whisk attachment, beat remaining 3 egg whites at medium-low speed until frothy, 1 to 2 minutes.
With machine running, gradually add remaining 3 tablespoons sugar, increase speed to medium-high, and beat until soft peaks form, 60 to 90 seconds.
Stir one-third of whites into batter to lighten; add remaining whites and gently fold into batter until no white streaks remain.
Pour batter into prepared pan and bake until toothpick or wooden skewer inserted into center of cake comes out clean, 30 to 40 minutes.
Cool in pan 10 minutes, then invert cake onto greased wire rack; peel off and discard parchment.
Invert cake again; cool completely, about 2 hours.
FOR THE STRAWBERRY FILLING:
Halve 24 of best-looking berries and reserve.
Quarter remaining berries; toss with 4 to 6 tablespoons sugar (depending on sweetness of berries) in medium bowl and let sit 1 hour, stirring occasionally.
Strain juices from berries and reserve (you should have about 1/2 cup).
In workbowl of food processor fitted with metal blade, give macerated berries five 1-second pulses (you should have about 1 1/2 cups).
In small saucepan over medium-high heat, simmer reserved juices and Kirsch until syrupy and reduced to about 3 tablespoons, 3 to 5 minutes.
Pour reduced syrup over macerated berries, add pinch of salt, and toss to combine.
Set aside until cake is cooled.
FOR THE WHIPPED CREAM:.
When cake has cooled, place cream cheese, sugar, vanilla, and salt in bowl of standing mixer fitted with whisk attachment.
Whisk at medium-high speed until light and fluffy, 1 to 2 minutes, scraping down bowl with rubber spatula as needed.
Reduce speed to low and add heavy cream in slow, steady stream; when almost fully combined, increase speed to medium-high and beat until mixture holds stiff peaks, 2 to 2 1/2 minutes more, scraping bowl as needed (you should have about 4 1/2 cups).
TO ASSEMBLE THE CAKE:
Using large serrated knife, slice cake into three even layers.
Place bottom layer on cardboard round or cake plate and arrange ring of 20 strawberry halves, cut sides down and stem ends facing out, around perimeter of cake layer.
Pour 1/2 of pureed berry mixture (about 3/4 cup) in center, then spread to cover any exposed cake.
Gently spread about one-third of whipped cream (about 1 1/2 cups) over berry layer, leaving 1/2-inch border from edge.
Place middle cake layer on top and press down gently (whipped cream layer should become flush with cake edge).
Repeat with 20 additional strawberry halves, remaining berry mixture, and half of remaining whipped cream; gently press last cake layer on top.
Spread remaining whipped cream over top; decorate with remaining cut strawberries.
Serve, or chill for up to 4 hours.
