In a stand mixer, cream the softened butter and the sugar together.

Add the egg and vanilla and beat on medium speed until mixed well, scraping the sides of the bowl as needed.

Add the flour and nutmeg. Mix just until combined, scraping down the sides once. Be careful not to overmix.

Form the dough into a thick log about 8 to 10 inches long. Press the log tightly together so that there are no air pockets in the dough.

Place a long sheet of plastic wrap on the counter and scatter sprinkles on it. Roll the log in the sprinkles until it is completely covered, adding more as needed.

Wrap the dough in the plastic wrap and refrigerate it for at least 2 hours.

Heat the oven to 325°F.

Unwrap the log. With a sharp knife, cut slices off the log, 1/4 inch thick or a little less. Place the slices on a baking sheet lined with a silicone mat, or on a lightly greased cookie sheet.

Bake for 10 to 12 minutes, just until the cookies are set. Do not let them brown.

Let the cookies cool on the baking sheet for 3 to 5 minutes, then move them to wire racks to cool completely. Store in an airtight container.