Beat egg yolks and sugar together in a large bowl until pale yellow in color.

Bring milk to a boil in a saucepan and remove from heat. Slowly stream milk into the egg mixture while beating with a whisk to integrate completely.

Pour milk mixture into the saucepan and place over low heat; cook, stirring constantly, until thickened but not yet boiling, about 10 minutes.

Stir red bean paste into the thickened milk mixture; pour into a large bowl and let cool for several minutes. Stir cream into the slightly cooled mixture until smooth.

Cover bowl with plastic wrap and refrigerate until ice cream base is chilled completely, 1 to 3 hours.

Pour mixture into an ice cream maker and freeze according to manufacturer direction.