If you have time to plan ahead, you can skip the step of cooking the banana peels, by freezing and thawing them to soften them. Remove the stem and very bottom of the banana peels, then cut the peels into 1-inch pieces and freeze in an airtight container in the freezer until you're ready to bake the cake. Thaw the peels, either in the refrigerator or the counter, depending on your timeline, and puree the peels as directed in step 4, adding up to 1/4 cup of water if needed. The peels will be nearly black, and thus the puree will not be pretty, but the final cake will be just as delicious. Banana peels contain some of the same proteins found in latex, and could cause an allergic reaction. Those same proteins might also make your immersion blender feel slightly gummy to the touch. Rub the surface down with cooking oil, and then wash it normally.