In a saucepan, heat the heavy cream and whole milk until steaming, stirring occasionally. Keep the heat gentle so it steams but does not boil, and remove from heat as soon as steam rises.

In a bowl, whisk the egg yolks with the granulated sugar until smooth and slightly thickened. Slowly pour the steaming dairy into the yolks while whisking to prevent scrambling.

Return the mixture to the saucepan and cook, stirring constantly, until it reaches 175°F. Cook to the exact temperature, then immediately remove from the heat.

Strain the custard into a clean container and stir in the bubblegum flavoring extract, vanilla extract, and salt. Mix until fully combined and glossy.

Add pink food coloring a little at a time until you reach your desired vivid pink color. Then cool the custard completely.

Refrigerate the cooled custard for 4 hours to fully chill. Chill until cold throughout before churning.

Churn the custard in an ice cream maker until thickened, then fold in the rainbow sprinkles and small bubblegum pieces during the last 2 minutes of churning. Watch for the mixture to turn fluffy and scoopable as you add the mix-ins.

Transfer the churned ice cream to a container and freeze until firm. Freeze until it holds its shape when scooped.