Marble Cheesecake Bars

1. 1Heat the oven to 325°F and arrange a rack in the middle.
2. 2Coat a 13-by-9-inch pan with butter. Place cookie crumbs and melted butter in a medium bowl and mix until thoroughly combined. Pour the crumb mixture into the pan and, using the bottom of a cup, press evenly into the bottom and slightly up the sides.

For the filling:

1. 1Combine chocolate and butter in a small saucepan and cook over low heat, stirring frequently, until evenly melted. Remove from heat and let cool to room temperature, about 15 minutes.
2. 2Whisk together sugar and flour in a medium bowl and set aside. Place cream cheese in the bowl of a stand mixer fitted with a paddle attachment and beat on medium speed until smooth, about 1 minute. With the mixer running, pour in sugar-flour mixture and beat until incorporated. Stop the mixer to scrape down the sides of the bowl and the paddle.
3. 3With the mixer on low, add vanilla and then 1 egg, allowing to incorporate completely. Stop the mixer to scrape down the sides of the bowl and the paddle. Return the mixer to low and repeat with remaining 2 eggs, allowing each to incorporate completely before adding the next.
4. 4Pour 2 3/4 cups of batter from the mixer into a medium bowl and reserve. Add cooled chocolate to the remaining batter in the mixer and beat on medium speed until evenly incorporated.
5. 5Randomly drop spoonfuls of chocolate batter over the prepared crust, then drop spoonfuls of reserved vanilla batter in between the chocolate. Drag a knife through the batter in a figure eight to create a marbled pattern. Bake until the outer 1 inch of batter is set and puffed but the center is slightly jiggly, about 25 to 30 minutes. Remove to a rack and let cool completely. Refrigerate until well chilled and firm, about 1 to 2 hours. Cut into squares and serve.