Puree blueberries in a blender or food processor until very smooth. Strain blueberry puree through a fine mesh sieve into a medium mixing bowl.
Add yogurt, half and half, sugar, and vanilla extract and stir until combined.
Pour mixture into popsicle molds. Depending upon the size of your molds, you can probably fill 4 to 6. If your popsicle mold does not have a lid, cover the top with foil and outline each well with your fingers. Cut a tiny slit in the middle of each well and insert popsicle stick.
Freeze for 4 hours or overnight, or until frozen solid.
When ready to serve, unmold popsicles. Briefly dipping molds in warm water helps the popsicles to cleanly release.