Arrange 12 paper cups on a small tray. Sprinkle ½ tablespoon of shredded coconut in the bottom of each cup. Pour 1 Tablespoon of coconut milk into each cup and swish until the shredded coconut is completely saturated. Place tray of cups in the freezer for at least 1.5 hours or until layer solidifies.
Meanwhile, in a small pitcher combine remaining 1 cup of coconut milk, 1.5 cups of cold brew and 3 teaspoons of sugar. Stir, cover and set aside.
Once the coconut milk layers are solid, remove tray from freezer and add about 3 tablespoons of your cold brew mixture to each cup. Cover each cup with foil and puncture with a wooden craft stick down the center. Stick the pops in the freezer for about six hours. Peel the paper away and enjoy!