Start by whisking the pudding mix with part of your milk in a bowl until smooth and thick. Make one batch of white chocolate (or vanilla) and one batch of chocolate pudding. Let them sit until slightly thickened but not fully set — this makes filling much easier.
Spoon alternating amounts of each pudding into a zip-top bag or directly into your popsicle molds. If using a bag, snip a small corner to pipe for neat swirls. This gives your pops that nostalgic multicolor look we all love.
Tap the filled molds gently to remove bubbles, insert sticks, and place in the freezer. Freeze at least 3 hours — or overnight if you can wait that long! When ready, dip the bottom of molds briefly in warm water to help release the pops