Insert ice-pop sticks into the cut end of the bananas, halfway up. Place on a baking sheet and freeze until firm, at least 4 hours.
Melt the chocolate in a double boiler, about 5 minutes.
Line a large baking sheet with wax paper and set aside. Dip the frozen bananas in the butterscotch and then sprinkle with candied nuts or sprinkles. Place on the prepared baking sheet and drizzle with melted chocolate. Place back in the freezer for at least 30 minutes to set.
Melt the butter in a medium saucepan over medium heat. Whisk in the brown sugar and salt. Cook, whisking continuously, until the sugar dissolves and caramelizes, about 5 minutes. Remove from the heat, carefully pour in the heavy cream, and then return to heat. Continue to cook until the mixture is smooth. Remove from the heat and let cool completely.
Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
In a medium bowl, whisk the egg white until frothy. Fold in the brown sugar and salt, and then the peanuts, pecans and walnuts. Spread in a single layer on the prepared baking sheet. Bake until toasted and the sugar has melted, about 10 minutes. Let cool to room temperature, then roughly chop.