Preheat oven to 300°F (150°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
In a large bowl, beat cream cheese, sugar, and flour until smooth.
Add sour cream and vanilla extract, mixing until combined.
Beat in eggs one at a time, ensuring each is fully incorporated.
Pour batter into the prepared pan. Place pan in a larger dish filled with hot water (water bath).
Bake for 50-60 minutes until center is just set. Let cool in oven, then refrigerate overnight.
Preheat oven to 350°F (175°C). Grease and line two 9-inch round cake pans with parchment paper.
Cream butter and sugar until fluffy. Mix in sour cream and strawberry extract.
Add egg whites one at a time, beating until just combined. In a separate bowl, whisk together flour, baking powder, and salt.
Add half of the dry ingredients, then milk and strawberry purée, then remaining dry ingredients. Mix until just blended. Fold in food coloring if using.
Divide batter between pans and bake for 25-30 minutes until toothpick comes out clean.
Beat cream cheese, heavy cream, powdered sugar, and vanilla extract until light and fluffy. Chill 1 hour.
To assemble, place a cake layer on a plate. Spread half the frosting. Repeat with second layer. Spread remaining frosting on top and sides.
Garnish with sliced and halved strawberries before serving.