Preheat oven to 350°F (175°C). In a bowl, combine flour, granulated sugar, brown sugar, and a pinch of salt. Cut in cold butter until the mixture resembles coarse crumbs. Mix in egg and milk until just combined. Pat into a 1-inch thick layer, cut into rounds, and place on a parchment-lined baking sheet. Brush with milk and sprinkle with sugar. Bake for 15-20 minutes until golden brown. Cool on a wire rack.

In a large bowl, cream together softened cream cheese and granulated sugar until light and fluffy. Add eggs one at a time, mixing well after each addition. Stir in vanilla extract. Pour the mixture into a springform pan over the cooled shortcake layer (broken into pieces if desired). Bake in a water bath at 325°F (160°C) for 45-60 minutes until the edges are set and the center slightly jiggles. Cool gradually.

Once cooled, layer pieces of shortcake into the cheesecake if not already added. Spread evenly with an offset spatula. Top with fresh strawberries, arranging them artfully.

In a chilled bowl, whip heavy cream, powdered sugar, and vanilla extract until stiff peaks form. Pipe or dollop onto the cheesecake.

Chill the cheesecake for at least 2 hours. Slice with a hot knife for clean cuts and serve cold.