Place strawberries and sugar in a food processor and pulse until the mixture is finely chopped and juicy, but still chunky as you don’t want a smooth puree.
Transfer to a bowl and stir in the balsamic vinegar and a few grinds of pepper if you choose.
Spoon the mixture into the ice pop molds and insert sticks in the middle.
Freeze until firm, approximately 6-8 hours.
To un-mold the pops, run hot water over the outside of the molds for a few seconds, then gently pull the sticks.