Preheat and prep: Preheat oven to 325°F (160°C) and place a large pan of water on the bottom oven rack. Line a 9x13-inch baking pan with parchment paper.
Make cookie crust: Pulse chocolate sandwich cookies in a food processor until fine crumbs. Mix with 3 tablespoons melted butter and 1/3 cup sugar. Press firmly into bottom and sides of the prepared pan.
Beat cream cheese: In a large bowl, beat cream cheese until creamy and fluffy.
Add sugar and eggs: Mix in 3/4 cup sugar. Add 3 eggs, one at a time, beating until incorporated.
Incorporate remaining filling ingredients: Stir in 3/4 cup sour cream, 1/2 teaspoon salt, 2 teaspoons vanilla extract, 3 tablespoons flour, and 1/2 cup Baileys Irish Cream. Mix until smooth.
Divide and color: Scoop 1 cup filling into two bowls. Add light green to one, dark green to the other, mixing until fully combined.
Assemble swirls: Pour white cheesecake filling evenly over crust. Drizzle alternating lines of light and dark green filling. Swirl gently with a knife or chopstick. Leave some white visible for a beautiful swirl pattern.
Bake: Bake 50–55 minutes until the center is just set. Open oven door and let bars sit for 1 hour.
Chill and serve: Refrigerate overnight for best slicing. Lift out with parchment, cut into squares, and serve.