Peel the bananas and insert one popsicle stick into the cut end of each banana, pushing it about halfway up.
Line a baking sheet with parchment paper and set it aside.
Place the white chocolate chips in a microwave-safe bowl and heat in 30-second bursts, stirring after each burst, until fully melted and smooth.
Dip each banana into the melted white chocolate, turning to coat all sides and leaving a small section near the stick uncovered.
Place the coated bananas on the prepared baking sheet.
Immediately press two mini chocolate chips into the white chocolate on each banana to form eyes.