In a saucepan, heat the heavy cream and whole milk until steaming, then slowly whisk the hot mixture into the egg yolks that have been beaten with the granulated sugar. Keep whisking to avoid scrambling the yolks, aiming for a smooth, glossy mixture.

Return the custard to the saucepan and cook, stirring constantly, until it reaches 175F. As soon as it thickens enough to coat a spoon, strain it and stir in the bubblegum flavoring extract, vanilla extract, and salt.

Stir in pink food coloring to reach your desired vivid bright pink color, then cool completely at room temperature before refrigerating for 4 hours. Chill until thoroughly cold so the custard churns smoothly.

Churn the chilled custard in an ice cream maker until it becomes a soft-serve consistency. For best flavor and texture, fold in the rainbow sprinkles and small bubblegum pieces during the last 2 minutes.

Transfer the churned ice cream to a container and freeze until firm. Freeze until scoopable with no wet pockets in the center.