Preheat your oven to 325°F and line a 9x13-inch baking dish with parchment paper.
In a food processor, pulse the Oreos into fine crumbs. Stir in the melted butter until everything is evenly mixed.
Press the crumb mixture firmly into the bottom of your pan to form the crust. Bake for 10 minutes, then let it cool completely.
While the crust cools, beat the softened cream cheese and sugar together until smooth and creamy.
Add in the sour cream and mix until well combined.
Add the eggs one at a time, mixing after each one.
Divide the cheesecake batter evenly into three bowls. Leave one bowl as-is (white), and color the other two with red and blue gel food coloring.
Spoon the three colors randomly over the cooled crust, then use a butter knife to swirl the colors for a fun tie-dye look.
Bake for 45–50 minutes, then let it cool to room temp before refrigerating for at least 6 hours (or overnight).