Line a baking sheet with parchment or a silicon baking mat.

Cut the apples lengthwise (stem to bottom) into 4 thick slices each. Remove any visible seeds and keep the core intact. The end slices will be rounded; cut a thin slice off so they lay flat. Poke a small hole in the bottom of each slice with a wooden ice-pop stick and push halfway into the apple.

Combine the dark chocolate and 1 teaspoon of the coconut oil in a medium microwave-safe bowl and microwave at 50 percent power for 30-second increments, stirring in between, until melted and smooth. Add the white chocolate and remaining 1 teaspoon coconut oil to another medium microwave-safe bowl and microwave at 50 percent power for 30-second increments, stirring in between, until melted and smooth.

Dip 4 of the apple slices completely in the dark chocolate, letting the excess drip back into the bowl, and place on the prepared baking sheet. Repeat with 4 apple slices in the white chocolate. Let sit at room temperature so the chocolate can thicken a bit, 10 to 15 minutes. Alternately you can slide them in the fridge for a few minutes to speed up the process.

Transfer the leftover dark and white chocolate to 2 separate small resealable plastic bags and snip a small corner off each bag. Pipe 3 to 4 dark chocolate circles, starting with a small one in the center and getting larger as you go towards the outside edge, on the white chocolate-dipped apples and white chocolate circles on the dark chocolate-dipped apples. Drag a toothpick through the circles, starting in the center and working your way out to create a spider web design. Refrigerate until hardened, 15 to 20 minutes.