Beat 16 ounces cream cheese in a large bowl on low speed until very smooth. You can use an electric mixer or wire whisk. If the cheese is at room temperature, mixing it by hand should not be a problem.
Gradually add ½ cup sugar and 2 tablespoons brown sugar and beat until well incorporated.
Add 3 eggs, mixing until incorporated and scraping down the sides of the bowl.
Add melted 12 ounces semisweet chocolate and 2 tablespoons unsalted butter and mix.
Add 1 teaspoon vanilla extract , ½ cup Baileys and ½ cup heavy cream, stirring to incorporate well.
Pour the batter into the prepared pan and smooth the top.
Bake for 10 minutes at 350°F (180°C), turn the oven down to 280ºF (140°C) and bake for another 40-45 minutes. (This can vary depending on your oven). At this point, the cheesecake should jiggle in the center. Don't be tempted to bake it longer.
Turn the oven off and, leaving the door ajar, let the cheesecake inside for 1 hour. The residual heat will keep on baking it.
Prepare the topping (below) a few minutes before taking it out of the oven. Spread it carefully almost touching the edges.
Cool to room temperature, wrap in plastic, and refrigerate for 8 to 12 hours. I recommend 1 day of refrigeration for the creamiest consistency.
Run a small knife around the edges to loosen up any bits that might be stuck, remove the cheesecake from the cake pan, transfer to the serving plate, and drizzle with chocolate ganache.
Keep leftovers refrigerated, covered in plastic wrap.