Add cherries and 1 Tbsp sugar to a small sauce pan over medium heat. Simmer for 5-7 minutes, stirring and breaking apart cherries with the back of a spoon. Transfer to a large mason jar or bowl and refrigerate to cool and thicken.
Meanwhile, add yogurt, half and half, goat cheese, remaining 2 Tbsp sugar and vanilla paste to a bowl and whisk until smooth.
Once the cherries have cooled, use an immersion blender to puree the mixture until smooth.
Alternate cherry puree and yogurt mixture in popsicle molds, swirling with a knife or wooden stick as you go. Cover, add sticks and freeze at least 6 hours (or until completely solid).