Preheat oven to 375°F and prepare a 9-inch springform pan with parchment paper and grease.
Combine flour, sugar, baking powder, and baking soda in a food processor.
Add butter and pulse until mixture resembles coarse crumbs.
Slowly add heavy cream and pulse until just moistened.
Gather dough into a ball and knead gently until smooth, about five turns.
Press dough evenly into the pan and bake for about 20 minutes until edges are golden.
Remove from oven and cool completely on a rack.
To make strawberry sauce, combine sugar and cornstarch in a saucepan; stir in strawberry puree and water.
Cook over medium heat, stirring constantly until thick and boiling, then boil for 1 minute.
Remove sauce from heat and cool completely.
Prepare springform pan again by washing, spraying with non-stick spray, reassembling with cooled shortcake.
Line inside edge of pan between shortcake and pan with parchment paper.
Slice 6 to 10 strawberries about the same size and arrange standing on edge against pan inside the shortcake.
In a large bowl, beat cream cheese and sugar until smooth.
In another bowl, whip heavy cream, powdered sugar, and vanilla to stiff peaks.
Fold whipped cream into cream cheese mixture gently until combined.
Spread half a cup of cheesecake filling over shortcake, making a thin layer.
Cut tops off 18-24 strawberries and arrange them top-down on the thin cheesecake layer spaced slightly apart.
Spoon remaining cheesecake filling over strawberries to fill spaces and spread evenly.
Refrigerate cheesecake for 4 to 5 hours until firm.
Remove cheesecake from pan and place on serving platter.
Whip cold cream, powdered sugar, and vanilla extract to stiff peaks.
Pipe whipped cream around outer top edge of cheesecake.
Slice remaining strawberries, arrange inside whipped cream, and top with cooled strawberry sauce.
Refrigerate until serving; store leftovers airtight in fridge for 3 to 4 days.