Blend the coconut milk, vanilla extract, and stevia until smooth.
Pour off about 1/3 of the mixture into a glass jar and refrigerate until needed.
Add the strawberries to the blender and pulse until fairly smooth but you still see flecks of fruit.
Fill the popsicle molds about 1/3 full with the strawberry mixture. Freeze for one hour.
Add the reserved coconut milk mixture to each mold as evenly as possible, filling about 2/3 full. Freeze one hour.
Fill molds to the top with strawberry mixture. Freeze 30 minutes. BE SURE TO SET A TIMER!
Insert the sticks by pushing into the partially frozen top layer about halfway down as evenly as possible (check that they are vertical).
Return to freezer and freeze at least one more hour, preferably overnight.
To unmold: Fill a tall glass 3/4 full with warm water. Hold each mold in the water, taking care to keep the edge of the mold above the water line. After approximately 45-60 seconds you will be able to pull the pop out. Have a ziptop freezer bag ready, and freeze pops as you unmold them.