Combine the pecans and rum in a small bowl and let soak at least 30 minutes.
Whisk the flour, nutmeg and salt in a medium bowl. Beat the butter and 1/2 cup confectioners¿ sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Add the pecan-rum mixture and the vanilla and beat until combined. Reduce the mixer speed to low and beat in the flour mixture, then increase the speed to medium high and beat until combined. Cover and refrigerate until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Roll tablespoonfuls of dough into 1-inch balls and arrange 1 inch apart on the prepared baking sheets. Bake until light golden, 20 to 25 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.
Put the remaining 1 cup confectioners¿ sugar in a medium bowl. Gently roll the cookies in the confectioners' sugar, returning to the racks as you go, then reroll the cookies to fully coat.