Line an 8-inch springform pan with parchment paper and grease the sides. Preheat the oven to 350°F (175°C).
In a medium bowl, whisk together flour, baking powder, and salt. In a larger bowl, beat the butter and sugar until fluffy (2-3 minutes). Add the eggs one at a time, then stir in the vanilla.
Gradually add the dry ingredients and milk, alternating between the two. Start and finish with dry ingredients. Pour the batter into the pan and smooth it out.
Bake for 20-25 minutes, or until a toothpick comes out clean. Let the cake cool completely.
Beat the softened cream cheese and powdered sugar until smooth. Add the vanilla and mix again. Slowly add the cold heavy cream and beat until fluffy (3-4 minutes).
Spread the cheesecake mixture evenly over the cooled cake. Place the cake in the fridge while you prepare the strawberry topping.
In a saucepan, cook the strawberries and sugar over medium heat until the berries release their juice. Add the cornstarch-water mixture and stir until it thickens, about 5-7 minutes. Remove from heat and let it cool slightly.
Spoon the strawberry topping over the cheesecake layer. Refrigerate for at least 2 hours, or up to 4 hours, to set.
Once chilled, remove the cake from the springform pan. Slice with a sharp knife, wiping the knife between cuts for clean slices.