Add sugar and continue whisking until mixture has thickened.
Add milk and heavy cream and whisk until combined.
Add bubblegum extract and food coloring until desired flavor and color is achieved.
Transfer mixture to the chilled bowl of an ice cream maker and churn until ice cream thickens and mixer slows or stops.
Scoop spoonfuls of thickened ice cream and layer with bubblegum balls into a freezer-safe container. (Be careful stirring in the bubblegum balls as the color will bleed.)