Mochi wrapper recipe more or less identical to recipes by Maangchi and use real butter (see their posts for step-by-step tutorials!) I divided the recipe into two halves for one batch each of green tea mochi and plain mochi — to make just one large batch, follow their recipes instead.
For the red bean paste, you can choose to strain out the biggest pieces of bean skin if you want to. Do so by pushing the mixture through a fine mesh strainer. I did one batch straining the skin and one batch with skin intact — the taste difference was negligible, if discernible at all.
For mochi ice cream, omit the red bean paste and use ice cream balls instead! Scoop ice cream into 1-tbsp balls and space evenly on a baking sheet. Replace in freezer and let chill until hard. Use in place of the red bean paste balls. Return to freezer after forming the mochi balls or enjoy immediately!