Heat the strawberries and honey in a small pot on medium heat and cook down for about 10 minutes, string frequently until the mixture begins to thicken and the strawberries release their juices. Mash the berries with a fork. Remove from heat and cool completely.
Whisk the vanilla Greek yogurt, milk and vanilla extract together in a bowl. If needed, add more milk to thin the yogurt out so the consistency is easy to pour into the popsicle molds.
Gently fold the cooled strawberry mixture into the yogurt and add to the popsicle mold. If a marbled or swirly pattern is desired, either do not overmix the strawberry and yogurt mixture OR alternate adding the yogurt mixture and strawberry mixture to the popsicle mold to create layers. Then use a knife to create a marble effect in the mold.
Place the cover on the mold and insert the popsicle sticks about ¾ of the down into the mold and freeze overnight until solid.
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