Preheat the oven to 350°F (175°C) and generously butter a 9-inch springform pan.
In a medium-sized bowl, combine the melted butter, crushed chocolate graham crackers, and granulated sugar until evenly mixed.
Firmly press the crust mixture into the bottom of the prepared pan and bake for 10 minutes. Let it cool while you prepare the filling.
In a large bowl, beat the cream cheese until smooth and creamy. Add in the sour cream, eggs, granulated sugar, half and half, and vanilla extract. Beat until fully combined with no lumps.
Pour the filling over the crust in the pan and smooth out the top with a spatula. Bake for 30-35 minutes, until the edges are set and slightly golden brown.
Let the cheesecake cool completely before chilling in the fridge for at least 2 hours. Prepare the chocolate ganache by heating heavy whipping cream in a saucepan until simmering, then adding chopped chocolate or chips until melted. Pour over chilled cheesecake and chill for 30 minutes before serving. Enjoy your decadent chocolate ganache cheesecake!