Step 1: Make the Cake Layer

1. Preheat your oven to 350°F (175°C). Butter a 9-inch springform pan generously, and wrap the outside of the pan with foil to prevent any leaks during baking. This is especially important since the cheesecake layer needs a water bath, and you don’t want any water seeping in.
2. In a medium bowl, sift the cake flour, baking powder, and salt. Sifting helps to aerate the flour and removes any lumps. Set the dry ingredients aside.
3. Using an electric mixer, beat the egg yolks and ⅓ cup sugar on high for about 3 minutes until the mixture becomes thick and forms light-yellow ribbons. This step is crucial as it helps to create a smooth, airy batter.
4. Add the vanilla extract to the egg yolk mixture and beat it in well.
5. Gradually sift the flour mixture over the egg yolk batter. Stir gently until the flour is fully incorporated, then add the melted butter and mix until smooth. It’s essential to combine the butter thoroughly to achieve the desired texture.
6. In a separate, clean bowl, beat the egg whites with cream of tartar on high until frothy. Gradually add the remaining 2 tablespoons of sugar and continue beating until stiff peaks form. When the egg whites are ready, they should stand up in stiff peaks but not be dry.
7. Gently fold ⅓ of the egg whites into the cake batter to lighten it. Then, carefully fold in the rest of the egg whites. Be as gentle as possible during this step to prevent deflating the air bubbles that make the cake layer fluffy.
8. Pour the batter into the prepared pan and bake for 13-15 minutes or until just set. The cake should be golden on top, and it should spring back lightly when touched. Be sure not to overbake the cake, or it might become dry.
9. Cool the cake on a wire rack while you prepare the cheesecake filling.

Step 2: Make the Cheesecake Layer

1. Beat one package of softened cream cheese, ⅓ cup sugar, and cornstarch in a large bowl with an electric mixer on low for about 3 minutes, until smooth and creamy. Be sure to scrape down the sides of the bowl regularly to ensure everything is well incorporated.
2. Add the remaining cream cheese and beat on high speed until well combined, about 2-3 minutes. The cheesecake batter should be smooth and creamy with no lumps.
3. Gradually add the remaining sugar and vanilla extract, and beat until fully incorporated.
4. Add the eggs, one at a time, beating well after each addition. It’s essential to add the eggs one at a time to prevent overmixing, which can cause the cheesecake to crack during baking.
5. Add the heavy cream and mix it into the batter until smooth and creamy.
6. Spoon the cheesecake filling over the cooled cake layer in the springform pan. Be careful not to disturb the cake layer as you spread the cheesecake filling.
7. Wrap the pan in foil and place it in a large shallow pan. Add hot water around the pan to about 1 inch up the sides. This water bath method helps cook the cheesecake gently and prevents cracking.
8. Bake for 75-85 minutes, or until the center barely jiggles when shaken. The cheesecake will continue to cook as it cools, so don’t worry if it seems a little soft when you take it out of the oven.
9. Cool the cheesecake on a wire rack for 1 hour. Then, cover the pan with plastic wrap and refrigerate for at least 4 hours or overnight to allow it to set properly.

Step 3: Make the Pastry Cream

1. In a large mixing bowl, combine the heavy cream, instant vanilla pudding mix, and milk. Use a whisk or an electric mixer to beat the mixture on high until it thickens into a custard-like consistency. It should hold its shape when you lift the whisk.
2. Spread or pipe the pastry cream onto the chilled cheesecake layer. You can use a spatula to spread it evenly or pipe it with a piping bag for a more decorative look.
3. Refrigerate the cheesecake again for at least 30 minutes to allow the pastry cream to set and firm up before adding the chocolate glaze.

Step 4: Make the Chocolate Glaze

1. In a microwave-safe bowl, combine the semisweet chocolate, corn syrup, and butter. Microwave the mixture in 30-second intervals, stirring each time, until everything is melted and smooth. Be careful not to overheat the chocolate, as it can seize up.
2. Let the glaze cool slightly before pouring it over the pastry cream layer. This prevents it from melting the cream underneath. Pour the glaze evenly over the top of the cake, making sure it covers the pastry cream.
3. Allow the glaze to set before serving. You can speed up this process by chilling the cake in the refrigerator for about 30 minutes.