Preheat oven to warm setting, about 180° F.
In a large pot with a lid, or 5-quart Dutch oven, bring water, maple syrup, rum, and salt to a boil over medium heat.
While the syrup is coming to a boil, start the dumpling dough.
Add flour, baking powder, baking soda, and salt to the bowl of a food processor. Pulse to combine.
Add the cold butter and pulse 6 to 8 times, or until it resembles a coarse meal.
Pour out into a bowl and add buttermilk. Stir until combined. (If dry, add another tablespoon of buttermilk.)
Use a spoon or small ice cream scoop and drop dough into the sauce. Fill the pot ⅔ full. Cover the pot with a lid, reduce heat to low, and simmer until cooked through, about 10 minutes.
Transfer the cooked dumplings to a dish and place in the warm oven.
Repeat with the remaining dough. If the sauce gets too thick, add a little water to thin it out.
Serve the dumplings warm with sauce, whipped cream or ice cream, and toasted pecans.