Preheat your oven to 350°F (175°C). Grease a baking dish (about 8×8 inches) or individual ramekins.
Prepare the pudding batter: In a large bowl, combine the flour, desiccated coconut, brown sugar, baking powder, and salt.
Add wet ingredients: Stir in the dairy-free yogurt, dairy-free buttermilk, vegetable oil, and vanilla extract until well combined. The batter should be smooth and thick.
Make the caramel sauce: In a separate bowl, mix together the brown sugar and cornstarch. Sprinkle this mixture evenly over the batter in the baking dish or ramekins.
Pour boiling water: Carefully pour the boiling water over the batter and sugar mixture. Do not stir. The water will sink to the bottom and create a sauce as it bakes.
Bake: Place the baking dish or ramekins on a baking sheet (to catch any spills) and bake in the preheated oven for 40-45 minutes, or until the top is golden brown and the pudding is set.
Serve: Allow the pudding to cool slightly before serving. Scoop out portions, making sure to get some of the caramel sauce from the bottom. Serve warm, optionally with dairy-free ice cream or whipped topping.