Preheat oven to 325°F (163°C). Line an 8x8-inch baking pan with parchment paper, leaving some overhang.
In a medium bowl, combine chocolate cookie crumbs, sugar, and melted butter. Press firmly into the bottom of the prepared pan to form an even crust.
Bake crust for 8-10 minutes. Let cool slightly.
In a large bowl, beat the cream cheese and sugar together until smooth and creamy.
Add sour cream, eggs, and vanilla extract, beating until fully combined.
Mix in cocoa powder until incorporated.
Stir in melted chocolate until the batter is smooth.
Pour cheesecake batter over the crust and smooth the top with a spatula.
Bake for 30-35 minutes, or until the center is set but still slightly jiggly.
Allow the bars to cool at room temperature for about 1 hour.
Refrigerate for at least 2 hours or overnight before slicing.
Drizzle with melted chocolate or sprinkle with chocolate shavings before serving, if desired.