Whisk all the ingredients, minus the gums, over medium heat. Make sure the egg yolks are well combined.
Add the pieces of pink bubble gum and bring to a light boil. Whisk until the gum softens and the base has thickened.
Remove from heat, cover, and place in the fridge until completely cold. At least 3 hours, but overnight is better.
Before pouring the ice cream base into the frozen bowl of an ice cream maker, place a paper towel in a colander and strain the base to remove of the gum particles.
Pour the base into an ice cream maker and churn for 20-30 minutes.
Once frozen, add the gumballs. Eat immediately or store in an air-tight container and freeze.