Preheat oven to 325°F. Line a 9-inch springform pan with parchment. Beat cream cheese until smooth. Add sugar, eggs, sour cream, and 1 tsp vanilla bean paste. Pour into pan.
Bake in a water bath for 45-50 minutes. Let cool in the turned-off oven for 1 hour, then chill overnight.
Preheat oven to 350°F. Whisk flour, sugar, baking powder, and salt. Cut in butter until sandy. Combine milk, egg whites, strawberry puree, and remaining vanilla, then fold into dry ingredients.
Divide batter between two 9-inch cake pans. Bake for 25-30 minutes. Let cool completely.
Beat the frosting butter until fluffy. Add powdered sugar, strawberry powder, and heavy cream. Whip until light and airy.
Assemble the cake: Place one strawberry cake layer down, top carefully with the chilled cheesecake layer, and finish with the second cake layer.
Frost the outside of the cake and press the Oreo crumbs into the sides. Chill for 2 hours before slicing.
