Preheat oven to 300°F and line a 9-inch springform pan with foil. In a large bowl, beat the room temperature cream cheese, 1 cup sugar, and 3 tbsp flour together until smooth and creamy, about 2 minutes. Stir in the sour cream and 1 tbsp vanilla extract until combined. Add the 3 eggs one at a time, mixing gently after each addition until just incorporated—overmixing can create a dense texture. Pour the batter into the prepared pan and place it inside a larger roasting pan. Fill the roasting pan with warm water halfway up the sides of the springform pan to create a water bath, which ensures even, gentle cooking and prevents cracking.
Bake the cheesecake at 300°F for 55 minutes until the edges are set but the center still jiggles slightly when gently shaken. Turn off the oven and crack the door open slightly, then leave the cheesecake inside for 30 minutes to allow it to cool gradually—this prevents the sudden temperature change that causes cracks. Open the door wider and leave it for another 30 minutes. Remove from the oven and water bath, then refrigerate for at least 5-6 hours or overnight. I prefer to make the cheesecake a day ahead so it's completely chilled and firm before assembly.
While the cheesecake chills, preheat oven to 350°F and prep two 8-inch round cake pans by lining them with parchment paper or greasing them well. In one bowl, whisk together 2.5 cups flour, 4 tsp baking powder, and 3/4 tsp salt and set aside. In a separate small cup, combine 1/2 cup whole milk and 1/2 cup strawberry puree and set aside. Having everything measured and ready before you start mixing ensures the batter comes together smoothly without overmixing.
In a large bowl, beat the softened butter and 1.5 cups sugar together for 2-3 minutes until light and fluffy, which incorporates air for a tender crumb. Mix in the 3/4 cup sour cream and 2 tbsp strawberry extract until combined. Alternately add the dry ingredient mixture from Step 3 and the milk-puree mixture from Step 3, beginning and ending with the dry mixture and stirring gently until just combined. Add 8 drops of pink food coloring and stir until the batter is evenly tinted. In a separate bowl, beat the 6 egg whites until stiff peaks form, then gently fold them into the batter in two additions using a spatula—this creates a lighter, more delicate cake texture.
Divide the strawberry cake batter from Step 4 evenly between the two prepared pans. Bake at 350°F for 27-30 minutes until a toothpick inserted in the center comes out clean and the tops spring back when lightly touched. Cool the cakes in their pans for 10 minutes, then turn them out onto wire racks to cool completely before assembly. For easier handling during assembly, I like to wrap the cooled cake layers loosely and chill them for 30 minutes so they're less fragile.
In a large bowl, beat the softened 16 oz cream cheese until smooth and creamy. In another bowl, beat the very cold 3 cups heavy whipping cream with 1.5 cups sifted powdered sugar, 1 tbsp vanilla extract, and 1/8 tsp salt until stiff peaks form. Gently fold the whipped cream mixture into the cream cheese in two additions until just combined and stiff—be careful not to deflate the whipped cream. The frosting should be thick and fluffy, perfect for layering and decorating.
Remove the chilled cheesecake from the springform pan by running a warm knife around the edges and carefully lifting out. Trim the tops of the two strawberry cake layers to create flat surfaces. Place the first cake layer on a serving plate or cake board and spread about 1 cup of frosting from Step 6 over it. Carefully place the cheesecake layer on top, then spread another 1 cup of frosting over it. Top with the second cake layer and spread the remaining frosting over the top and sides of the assembled cake, smoothing it with an offset spatula or the back of a spoon. Arrange 15-20 fresh whole strawberries decoratively on top of the cake just before serving. The cake can be refrigerated for up to 2 hours before serving to help it hold its shape.