Prepare Oreo Crust:
Preheat oven to 350°F (175°C). Grease and line an 8-inch springform pan. Mix crushed Oreos with melted butter until combined. Press firmly into pan bottom. Bake for exactly 10 minutes. Cool completely.
Make Cream Cheese Base:
Beat softened cream cheese on medium speed for 3 minutes until smooth. Gradually add granulated sugar, mixing 2 more minutes. Add vanilla extract and combine.
Whip Cream:
In a separate bowl, whip heavy cream and powdered sugar to stiff peaks (~3-4 minutes). Fold gently into cream cheese mixture.
Divide & Color:
Divide mixture equally into six bowls. Add gel food coloring by drop to achieve red, orange, yellow, green, blue, and purple. Mix thoroughly.
Layer & Swirl:
Dollop colored mixtures randomly over crust. Use a knife to swirl gently in up to three figure-eight motions to create marbled rainbow pattern.
Chill:
Refrigerate for at least 4 hours to set.
Prepare Ganache Drip:
Heat milk and remaining cream until warm. Add food coloring and powdered sugar as needed for drip consistency. Cool slightly before pouring over chilled cake.
Serve:
Add desired decorations and slice to serve.