Line a baking sheet with parchment paper and set it aside.

Place the semi-sweet chocolate chips and 1/2 teaspoon of the coconut oil in a microwave-safe bowl. Heat in 30-second bursts, stirring after each, until fully melted and smooth.

Pour the melted semi-sweet chocolate onto the prepared baking sheet and spread it into an even layer about 1/4 inch thick.

Place the white chocolate chips and remaining 1/2 teaspoon coconut oil in a separate microwave-safe bowl. Heat in 20-second bursts, stirring after each, until melted and smooth.

Drizzle the white chocolate over the dark chocolate layer in several concentric circles. Use a toothpick to drag lines from the center outward, creating a spiderweb design.

Let the bark sit at room temperature until fully set, then break it into pieces.