Pour milk and bubblegum extract into a medium size saucepan and bring to a simmer, where the milk is bubbling along the edges of the saucepan.
In a small bowl combine the egg yolks with the sugar, stir together. Take 1/2 cup of the warmed milk and pour in a steady stream into the eggs while whisking to prevent curdling.
Add the egg mixture to the milk in the saucepan and continue cooking over medium, while whisking, for 5-7 minutes until the mixture is thickened.
Remove mixture from heat and pour into a large bowl over ice to chill. Stir in heavy cream, vanilla extract and blue food coloring if desired. Let chill for 20 minutes, or cover and place in refrigerator for at least 2 hours until chilled.
Add to your ice cream mixer for churning.
Churn ice cream for about 15 minutes, add in the gumballs, continue to churn for another 5 minutes. The consistency will be soft. Place ice cream in a sealed container and freeze for about 2 hours prior to serving.