Place the halved peaches cut side up on a baking sheet. Drizzle 2 tablespoons of honey over the peaches. Roast the peaches for 20 minutes until tender.
Transfer the roasted peaches to a blender or food processor and blend until smooth. Pour the puréed peaches into a medium bowl.
In a separate bowl, mix together the yogurt, remaining 2 tablespoons of honey, and vanilla extract.
Gently swirl the yogurt into the peach mixture (for the marbled effect, be sure not to over mix - just swirl enough to distribute the yogurt).
Use a funnel to fill each popsicle mold with the peachy popsicle mix. (Note: Fill just under full because it will expand a bit when it freezes, which can make the lid difficult to remove).
Place the lid over the mold and insert your popsicle sticks as straight at possible.
Freeze for 4-6 hours, or until frozen solid. For best results, freeze over night.
To help remove your popsicles from the mold, fill a large bowl with warm water and briefly dunk the bottom part of the mold in the bowl or briefly run the mold under running warm water.