Preheat the oven to 325°F (160°C).
Prepare a 9x13-inch baking dish by greasing it or lining it with parchment paper.
In a medium bowl, combine the graham cracker crumbs and melted butter, mixing until evenly combined.
Press the graham cracker mixture firmly into the bottom of the prepared baking dish to form a crust.
Bake the crust in the preheated oven for 10 minutes, then remove and let it cool slightly.
In a large bowl, beat the softened cream cheese and powdered sugar until smooth and creamy.
Add the eggs one at a time, mixing well after each addition until fully incorporated.
Stir in the melted chocolate, Baileys Irish Cream, and vanilla extract until the mixture is fully combined.
Pour the cheesecake filling over the cooled crust and smooth the top with a spatula.
Bake the cheesecake bars for 30-35 minutes, or until the edges are set but the center is slightly jiggly.
Let the bars cool at room temperature for about an hour, then refrigerate for at least 4 hours before cutting.
Cut into squares and serve as desired, enjoying the rich flavors of Baileys and chocolate.