Preheat the oven to 325°F (163°C). Grease a 9-inch springform pan.
In a medium bowl, combine the graham cracker crumbs, 1/4 cup sugar, and melted butter until the mixture resembles wet sand. Press firmly into the bottom of the prepared pan.
Bake for 10 minutes, then remove and let cool while preparing the filling.
In a large bowl, beat the softened cream cheese and 1 cup sugar until very smooth and creamy, scraping down the sides as needed.
Add the eggs one at a time, beating well after each addition.
Mix in the sour cream and vanilla extract just until combined and smooth.
Pour the cheesecake filling over the cooled crust and smooth the top.
Bake at 325°F (163°C) for 55–60 minutes, or until the center is mostly set and only slightly wobbly in the middle.
Turn off the oven, crack the door slightly, and let the cheesecake cool in the oven for 1 hour to help prevent cracking.
Remove from the oven, cool to room temperature, then refrigerate for at least 4 hours or overnight until fully chilled and firm.
In a medium saucepan, heat the milk over medium heat until just starting to simmer.
In a separate bowl, whisk together the 1/2 cup sugar, cornstarch, and egg yolks until smooth and pale.
Slowly pour the hot milk into the egg mixture in a thin stream while whisking constantly to temper the eggs.
Return the mixture to the saucepan and cook over medium heat, stirring constantly, until thickened and bubbling.
Remove from heat and stir in the butter and vanilla extract until smooth.
Transfer the pastry cream to a clean bowl, press plastic wrap directly onto the surface to prevent a skin from forming, and cool completely in the refrigerator.
Once cool, spread the pastry cream evenly over the chilled cheesecake.
In a small saucepan, heat the heavy cream over medium heat until just simmering (do not boil).
Place the chopped semi-sweet chocolate in a heatproof bowl. Pour the hot cream over the chocolate and let it sit for 5 minutes.
Stir gently until the mixture is smooth and glossy.
Pour the ganache over the pastry cream layer, tilting the pan slightly to spread it evenly over the top.
Refrigerate the cheesecake for at least 1 hour to allow the ganache to set before serving.