Place the coconut milk, banana, vanilla, honey, and cocoa powder in a blender. Blend until very smooth.
Add berry slices to each of the molds you are using for the popsicles. If you don't have popsicle molds, you can use small paper cups for these. I used a Norpro mold that makes 10, 3-ounce pops.
Pour the cocoa mix slowly into the molds so it will settle around the berries. Gently tap the molds on the counter to fill in air pockets, and top with more cocoa mixture until your molds are almost full (the mixture will expand as it freezes, so leave a little room at the top). Insert wooden sticks (the strawberries should keep them in place) and freeze overnight, or until frozen through.