Line a cookie sheet with a silicone baking mat. Place in freezer until ready to use.
Make double-boiler by placing heat-proof bowl over a saucepan with simmering water. Make sure the bottom of the bowl doesn’t touch the water. Place white chocolate chips in the bowl and stir until melted and smooth.
Once melted, transfer half of the melted chocolate to another bowl. Working quickly, stir in pumpkin spice and puree. Mix until fully incorporated.
Remove lined cookie sheet from the freezer and pour pumpkin layer onto the center of the mat. Using an offset spatula or a silicone spatula, quickly spread the mixture into a thin layer.
Return to freezer and allow to solidify for about 10 minutes.
Meanwhile, set aside a few tablespoons of melted white chocolate. Add instant espresso powder to the remaining melted chocolate and stir until well incorporated.
When the pumpkin layer is somewhat solid, remove from the freezer. Pour the coffee layer over top of the pumpkin layer and smooth evenly over top.
Again, return to the freezer for another 10-15 minutes or until solid.
Once it is cold, you will be able to peel it from the mat as one solid piece. I flipped mine over and drizzled it with reserved white chocolate just to make it pretty. This is totally optional. If you decide to do the same, return it to the freezer for a few minutes after drizzling to let the final white chocolate set.
Remove from freezer and break into pieces. The bark will begin to soften a bit as it comes to room temperature, so keep it refrigerated and serve right before eating.