1. To make the crust, position a rack in the center of the oven and preheat to 350ºF (175ºC). Lightly spray a 12-by-4-inch (30-by-10-cm) rectangular tart pan or a 9-inch (23-cm) round tart pan with a removable bottom with cooking spray or brush it with a teaspoon of melted coconut oil.
2. In the bowl of a stand mixer fitted with the paddle attachment, combine the almond, sweet rice, and coconut flours with the sugar and salt. Scatter the coconut oil in clumps over the top and drizzle with the vanilla extract. Beat on medium-low speed until the coconut oil is evenly incorporated and the dough looks clumpy, 2 to 3 minutes. With the mixer running, slowly drizzle in the cold water, mixing until the dough comes together in large clumps. Dump the crumbly dough into the prepared tart pan and press the dough evenly into the pan, starting with the sides and then moving to the bottom, keeping the edges square. Prick the bottom of the crust all over with the tines of a fork and freeze until firm, 15 to 30 minutes.
3. Place the tart pan on a rimmed baking sheet and bake until golden all over, 20 to 25 minutes. Remove the crust from the oven and, while it's still hot, scatter the chopped chocolate over the bottom of the crust. Let the chocolate melt, 1 minute, then use the back of a small spoon to spread the melted chocolate over the bottom and up the sides of the crust. Let cool to room temperature, then chill until the chocolate is set, 10 to 20 minutes.
4. To make the filling, combine the coconut milk and vanilla pod and scrapings in a medium-size, heavy-bottomed saucepan. Heat over medium heat, stirring occasionally, until the milk is hot and steamy (don't let it boil or it may scorch or separate). Remove from the heat, cover, and let steep for 10 minutes or up to 1 hour to infuse with the vanilla.
5. Meanwhile, whisk together the sugar, cornstarch, and salt in a small bowl. When the coconut milk has steeped, whisk a few tablespoons of the coconut milk into the cornstarch mixture to make a slurry, then whisk the slurry into the warm coconut milk. Cook the pudding over medium heat, whisking constantly and making sure to scrape the bottom and corners of the pot, until it comes to a low boil. Still stirring, boil for 1 to 2 minutes; it should be the texture of yogurt. Immediately strain the pudding through a mesh sieve and into a heatproof measuring pitcher. Pour the hot coconut cream into the chocolate-lined tart shell, spreading it evenly and taking care not to disturb the melty chocolate. Chill until set, 2 hours.
6. When ready to serve, release the sides from the pan by pushing the tart bottom upward, and slide the tart onto a large cutting board. Top the tart with the raspberries. Cut into pieces and serve.