Combine bananas and yogurt in a blender or small bowl (if, like me, using a hand blender to mix). Heat the chocolate until it is just melted (about 30 seconds in the microwave). Pour ¾ of the chocolate over the bananas and yogurt, reserving the remaining melted chocolate, and blend banana mixture until smooth and creamy.
Pour the banana mixture evenly into popsicle containers, leaving about ½ inch at the top of each. Top each container off with a spoonful of the remaining melted chocolate. Add the popsicle sticks and freeze until solid, about 4 hours.
I like to finish off each popsicle with a dollop of pure chocolate which tends to drift down to the center of the popsicle to make a solid chocolate core, but they are just as good with all of the melted chocolate mixed in with the bananas.