In a small bowl, combine cornstarch with 3 tablespoon of coconut milk, stirring until smooth. Set aside.
In a medium saucepan, combine the remainder of coconut milk with 4 tablespoon of the coconut palm sugar and vanilla extract over medium heat. Add the cornstarch slurry.
Cook, stirring constantly until thickened. This may take up to 8-10 minutes.
Remove from heat. Cover with plastic wrap, pressing the wrap to the surface to prevent a skin from forming. Set aside.
Combine the blackberries with 2 tablespoon coconut palm sugar in a bowl or large measuring cup. Use an immersion blender to puree until it is mostly smooth. Alternatively use a regular blender.
Add ⅔ of blackberry puree to the coconut milk mixture. Mix well or use an immersion blender to combine them.
Pour creamy mixture into each well of the popsicle mold, filling them about ¾ full.
Top off each well with the plain blackberry puree, leaving about ½”/12mm space at the top. Using a butter knife, swirl through each of the wells to create a blended pattern.
Place the cover on the popsicle mold if it has one. Place a popsicle stick in the center of each well, leaving about 1 ½”/4cm of stick exposed.
Freeze for at least 8 hours.