Preheat your oven to 350 degrees F. Sprinkle the shredded coconut onto a rimmed baking sheet and toast in the oven for about 3 to 5 minutes, or until golden brown. Remove from the oven and set aside.
Place the strawberries into the bowl of a food processor. Add 2 tablespoons sugar and juice of half a lime. Blend until smooth.
Using a small mixing bowl, stir together the coconut milk, remaining lime juice, the remaining 2 tablespoons granulated sugar, and vanilla extract and stir in the toasted coconut.
Pour in some of the strawberry mixture into the bottom of each popsicle mold. Next, drizzle the slightly melted peanut butter over the top, and then pour in the coconut milk mixture to fill the each popsicle mold about 2/3rd full.
Cover with the popsicle mold lid and place sticks inside. Freeze for at least 8 hours, or overnight, before serving. When ready to serve, run the popsicle mold under warm water to help release the pops from the mold. Alternatively, you can place the popsicle mold in a large container filled with very warm water to loosen the pops. Enjoy!