The Big Difference Between Mashed Potato & Mashed Banana
One of the Av Milachos is Tochein, grinding, or making food into very little pieces. The Orchos Shabbos (1:5:9-13) says that mashing something, even if it remains in one clump and not separate pieces, is considered Tochein.
He brings from the Rambam that if something, like a potato, became very soft (it must be very soft according to Rav Shlomo Zalman Auerbach) from cooking it is already considered ground and therefore you may mash it. However you must mash it with a fork or spoon and not a special mashing utensil because it would be Uvda D'Chol.
This, he says, only applies to cooked foods but if a banana or avocado become soft without cooking, the issur of grinding still applies. He brings in the footnotes that Rav Moshe Feinstein in the Igros Moshe (4:74) matirs mashing a banana because it remains a single mass and not separate pieces. The Tosefta explicitly says that figs may not be mashed, but Rav Moshe says that his research shows that a fig comes apart while the banana doesn't.
Important Note: We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation. Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.