Heat the oven to 350 degrees. Place a 10-inch nonstick Bundt pan in the oven to preheat.

To a medium saucepan over medium heat, add the pumpkin purée and pumpkin spice. Cook, stirring frequently, until a film forms on the bottom of the pan and the pumpkin purée is smooth and glossy, 6 to 8 minutes. Turn off the heat.

To the saucepan, add the sugar, coconut milk, vanilla and salt. Place over medium heat and whisk for 1 minute until the sugar has dissolved. (Avoid bringing the mixture to a boil.) Set aside to cool slightly.

Place a large, fine-mesh sieve over a large bowl. Add the tapioca starch, rice flour and baking powder and sift, then whisk to combine. Place the sieve over another large bowl. Add the eggs to the sieve. Using a silicone spatula, gently mix the eggs to pass through the sieve, using delicate, long stirring motions to incorporate as little air as possible. This process will take a few minutes.

Pour the warm (or room temperature) pumpkin mixture through the sieve over the eggs, then gently whisk to combine.

Place the sieve over the dry ingredients. Pour the pumpkin-egg mixture over the dry ingredients. Gently whisk just until a mostly liquid batter forms, with many dry flour lumps all over.

Place the sieve over the empty bowl and pour the batter through, gently pushing the batter with a silicone spatula through the sieve. Repeat one more time until batter is completely smooth, with no flour lumps. Stir in 2 tablespoons of melted coconut oil.

To the preheated Bundt pan, add 1 teaspoon of coconut oil and brush the pan to coat. Pour the batter in the pan.

Bake, without opening the oven door for the first hour, until the cake looks golden and feels springy on top, 1 ¼ hours to 1 ½ hours. (When the cake is done, a toothpick inserted into its center should come out clean, without any raw batter.) Allow the cake to rest for 10 minutes in the pan, then carefully flip onto a serving plate. Let cool to room temperature.

To a small microwave-safe bowl, add the white chocolate and the remaining 2 teaspoons of coconut oil. Microwave, stirring at 15-seconds intervals, until ¾ of the chocolate is melted. Mix to combine, using the residual heat to melt the chocolate.

Slowly drizzle the melted chocolate on the cake, going in circles around the cake, slowly pushing the chocolate toward the sides. Using a small sieve, lightly sprinkle with more pumpkin spice on top. (The cake is best served fresh the day of, but can be stored at room temperature, covered, up to 3 days.)