In a saucepot (ideally at least 3 quarts/3.5L), whisk together all ice cream ingredients including red bean paste. Cook over medium heat and bring the mixture up to 170°F, stirring frequently.
At this stage you have a few options for the texture of the ice cream:A. Traditional. Blend until desired texture, leaving the skins in the base.B. Smooth. Blend until smooth, strain to remove skins.C. Chunky. Stir in 3/4 of red bean paste. Swirl the remaining 1/4 into the finished quart. Prepare an ice bath by filling a large container with equal parts ice and water with enough room to place a container containing the ice cream base inside. Pour the ice cream base into a large container set over an ice bath. Chill the mixture until very cold, below 40°F, adding more ice and stirring as needed.
Pour the ice cream base into an ice cream machine and spin according to machine directions. The resulting ice cream should be a smooth, soft-serve consistency. Transfer the ice cream to a storage container and freeze for at least 3 hours to fully firm up.