Cook the strawberry reduction: Puree the strawberries, then pour into a small saucepan with the lemon zest. Simmer over medium heat, stirring often, until reduced to about 1/3 cup and thick like a loose jam, 10–15 minutes. Scrape into a bowl and cool completely.
Bake the cheesecake: Heat oven to 305°F (152°C). Line a 9-inch springform pan with parchment on the bottom and a strip up the sides; lightly grease. Place a roasting pan on the lower rack and fill it halfway with hot tap water to create steam.
Make cheesecake batter: In a mixer on medium-low, beat cream cheese and sugar until smooth, about 1 minute. Mix in the flour. Add sour cream and vanilla and blend just until combined. Lightly whisk the eggs and yolk together, then stream them into the bowl on low speed until no streaks remain. Do not aerate.
Bake until set at the edges and slightly wobbly in the center, 50–55 minutes. Turn off the oven, prop the door open an inch, and rest the cheesecake inside for 20 minutes. Cool on a rack to room temperature, then refrigerate at least 3 hours (overnight preferred).
Prepare for cake layers: Raise oven temperature to 340°F (171°C). Grease two 9-inch round cake pans, line bottoms with parchment, and lightly grease the parchment. If you have baking strips, use them for flatter layers.
Reverse-cream the dry ingredients: In a stand mixer bowl, whisk flour, baking powder, and salt. Add the softened butter and mix on low until the mixture looks like damp sand, 1–2 minutes.
Combine the wet mixture: In a large measuring jug, whisk together sugar, milk, sour cream, strawberry extract, and 1/3 cup cooled strawberry reduction until smooth and pink.
Build the batter: Pour in half of the wet mixture and beat on low for 30 seconds. Add the rest and mix 45–60 seconds more, scraping once, until the batter is pale and slightly thick but not overworked.
Whip and fold egg whites: In a clean bowl, whip egg whites to soft, glossy peaks. Gently fold into the batter in two additions until just combined and no white streaks remain.
Bake the cakes: Divide batter evenly between pans, smooth tops, and tap to release air. Bake 24–27 minutes, or until a toothpick comes out with a few moist crumbs. Cool 10 minutes in pans, then turn out to a rack to cool completely. Level if needed.
Make the frosting: In a chilled bowl, whip cold cream, powdered sugar, and vanilla to soft peaks. In a separate bowl, beat cream cheese until completely smooth. Add cream cheese and salt to the whipped cream and beat on medium just until firm peaks form. If it gets too thick, whisk in 1–2 teaspoons of cream to loosen.
Assemble, part 1: Place one cake layer on a board. Spread a thin layer of frosting over the surface. Arrange a ring of sliced strawberries around the outer edge, scatter a few in the center, and top with about 3/4 cup frosting, smoothing flat.
Add the cheesecake: Release the chilled cheesecake from the pan. If it’s wider than the cake, trim the edge with a warm knife. Set it on the first layer, then spread another 3/4 cup frosting on top.
Finish assembly: Place the second cake layer on top. Apply a thin crumb coat over the whole cake and chill for 15–20 minutes. Cover with a smooth final coat, then pipe swirls around the edge with a large open star tip. Nestle halved strawberries into the swirls and press remaining slices around the base. Chill 30 minutes before slicing.