In a small saucepan, combine 1 cup of the heavy cream with the milk, sugar, and salt. Warm until the sugar and salt are dissolved.
In a large bowl, pour the remaining 1 cup heavy cream, and set a mesh strainer on top of the bowl.
In a medium bowl, whisk together the egg yolks. While whisking the yolks vigorously, slowly pour a couple ladles-full of the warm cream/sugar mixture into the yolks. Once tempered, slowly whisk the hot yolk/cream mixture back into the saucepan, and stir.
Continue to heat until the mixture thickens slightly, or reaches 165º on an instant-read thermometer. Remove from heat, pour through strainer into the remaining cup of heavy cream, and stir in the vanilla. Cool mixture over an ice bath, and then chill for several hours (or overnight) in the refrigerator.
When you are ready to churn, place the bananas, lime juice, and about 1 cup of the chilled ice cream base into a blender or food processor. Purée together until smooth. Stir the purée back into the rest of the ice cream base. Pour into your ice cream maker (there is usually a little leftover after my maker is filled — I pour the extra into a couple popsicle molds for banana ice-cream popsicles), and freeze according to the directions for your maker.
For the marshmallow creme (I adapted In large mixer bowl, use a whisk attachment to combine egg whites, corn syrup, and salt. Beat for 10 minutes until thick. (After only a minute or so, it begins to fluff up, but keep beating!)
Add powdered sugar at a low speed to thoroughly incorporate. Add vanilla extract and beat until well blended.
Refrigerate for up to a week or freeze for up to a month (it’s usable right out of the freezer, as it doesn’t harden, so freezing is your best bet).
To put it all together :
vanilla wafer cookies (I like the 365 brand from Whole Foods), broken into halves or quarters.
In a 1 1/2-quart air-tight container, scrape about 1/4 of the churned ice cream. Add 2-Tbsp dollops of marshmallow cream over the surface, and then scatter cookies on top. Layer in more ice cream, then more marshmallow creme and cookies, repeating the process 2-3 more times (finish with a layer of ice cream). Press plastic wrap or wax paper directly on the surface of the ice cream, seal with lid, and freeze for several hours before enjoying.