1. For the millet: Place a medium saucepan over medium heat and add the butter. When the butter melts, add the millet and cinnamon stick. Cook, stirring the millet so that it toasts evenly in the butter, about 3 minutes. Add 1 3/4 cups water and the salt. When the water comes to a boil, lower the heat, cover and simmer for 25 minutes. Fluff the millet with a fork and transfer to a bowl to cool completely.
2. For the mango and ginger syrup: While the millet is cooking, put the sugar, ginger, scraped vanilla seeds and pod, salt and 2/3 cup water in a small saucepan and bring to a boil. Lower the heat and simmer until the sugar dissolves and the liquid thickens a bit, about 15 minutes. Remove from the heat and immediately throw in the mango. Set aside to cool. Remove the ginger coins and vanilla pod before serving.
3. For the buttermilk: Whisk together the buttermilk, sugar and nutmeg in a medium bowl or pitcher until the sugar dissolves completely. Refrigerate until serving.
4. Spoon the millet into 6 small bowls and top each serving with about 1/2 cup buttermilk. Spoon some mango on top and drizzle with some of the syrup.