Position a rack in the center of the oven and preheat to 350 degrees.
In the bowl of the stand mixer fitted with the paddle attachment, combine the sweet rice and almond flours with the cocoa powder, tapioca starch, sugar and salt. Scatter the butter pieces over the top and drizzle with the vanilla extract. Turn the mixer to medium-low and run until the dough comes together in clumps and the butter is worked through, 3-5 minutes.
Transfer the crust mixture into a 9-inch round tart pan or pie plate. Press crust evenly onto the bottom and sides of the pan. Place the pan on a rimmed baking sheet and bake for 10 minutes.
Meanwhile, melt the dark chocolate by placing in a heatproof bowl a top a pot of simmering water. Stir chocolate until completely melted. Drizzle chocolate over crust. You can carefully spread the chocolate evenly across the crust using a spatula or the back of a spoon. Be careful not to rip the crust. Transfer the crust onto a room temperature sheet pan and chill the crust in the freezer for 15 - 20 minutes to harden the chocolate.
In a medium saucepan, whisk all filling ingredients over medium heat until smooth and warmed through. Do not bring to a simmer. Carefully pour over crust, being careful not to overfill and bake for 45 to 55 minutes, until the filling is set, but jiggles like jello. Let cool and serve, or chill in the fridge, covered, for up to 2 days until ready to serve.