Line 2 baking sheets with parchment.
Put the almonds and 1/2 cup of the confectioners' sugar in the bowl of a food processor and process until very finely ground, about 2 minutes. Add the butter and process until smooth, 30 seconds to 1 minute. Scrape the dough off the inside of the bowl if needed. Add the bourbon and rum and vanilla extracts and pulse until smooth. Add the flour and salt and pulse until the dough forms a ball.
Roll mounded teaspoons of the dough into balls about 1 inch wide and place on the prepared baking sheets about 1 inch apart. Refrigerate for 30 minutes.
Meanwhile, position oven racks in the top and bottom thirds of the oven and preheat to 350 degrees F.
Bake, rotating the baking sheets from top to bottom and front to back halfway through, until the cookies are firm when gently pressed, completely dry and just beginning to crack at the top, 20 to 25 minutes. Cool the cookies on the sheets for 5 minutes; they will firm as they cool.
Meanwhile, put the nutmeg and remaining 1 1/2 cups confectioners' sugar in a pie plate or wide baking dish and mix well. Toss the warm cookies very gently in the sugar mixture until evenly coated; the cookies need to be warm for the first coating of sugar to stick. Cool the cookies on a wire rack completely, about 30 minutes, then toss again in the sugar mixture so they are very white. Sprinkle with additional grated nutmeg.
Store the cookies in a little bit of extra confectioners' sugar in an airtight container for up to a week.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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