Insert 1 ice pop stick into the cut end of each banana half. Place the bananas on a wax paper-covered baking sheet, and freeze until the bananas are frozen through, about 2 hours.
Remove the frozen bananas from the freezer and spread a layer of peanut butter on each banana. Place the peanut butter-covered bananas back in the freezer for 30 to 45 minutes.
Melt the chocolate in the top of a double boiler over just-barely simmering water, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching.
Dip each frozen banana in the melted chocolate, spooning the chocolate over the banana to cover it completely. Roll the dipped bananas in the chopped peanuts and place on the wax paper covered baking sheet; freeze until the chocolate is firm, about 1 to 2 hours.