With a mixer, beat heavy whipping cream until thick. Pour in sweetened condensed milk, vanilla and birthday cake flavored oil and fold in until smooth.
Divide ice cream into 6 bowls, adding gel food coloring into 5 of them to create a rainbow effect for the ice cream. You can leave one bowl white if you choose.
Next, spoon ice cream into a freezer safe container, alternating colors by spoonful drops into the container.
Freeze for 5-6 hours or overnight. When it is time to serve, remove the container from the freezer and let sit on the counter for 5-10 minutes before serving.