Heat a medium saucepan on medium. Add cherries and 1 tbsp water and bring to a simmer. Cook until cherries soften and begin to release juices, 7 to 8 minutes. Remove from heat. Set aside to cool for a minimum of 10 minutes.
Meanwhile, in a blender, blend cheese, milk, honey and vanilla on low speed until beginning to smooth, increase speed to medium-high and blend and blend until thick and completely smooth. Transfer mixture to a small bowl and set aside. Wash blender.
In blender, blend cherry mixture on medium to medium-high speed until smooth. (TIP: When blending hot ingredients, remove plastic stopper from lid of blender and cover with a kitchen towel to allow steam to escape.)
Layer ingredients: To each mold, add about 2 tbsp cherries, followed by about 2 tbsp cheese mixture. Repeat with another equal layer of cherries and cheese mixture, insert sticks into center of each ice pop, pushing down to bottom. Freeze until completely set, at least 3 hours.