Stir together the flour, baking powder, nutmeg and salt in a medium bowl. Combine the butter and sugar in a mixer fitted with the paddle attachment and beat on medium-high speed until light and fluffy, 1 to 2 minutes. Scrape down the side of the bowl and add the egg and vanilla. Beat until smooth and fluffy, about 1 minute. Add the flour mixture and beat on low, scraping the bowl once, to make a smooth dough.
Remove the dough from the mixer and divide in half. Add the orange zest and orange gel food coloring to one half of the dough, kneading to incorporate, but don't incorporate the food coloring fully, in order to achieve a marbled look. Knead the teal food coloring into the other half of the dough. Wrap and refrigerate the teal dough.
Lay a piece of parchment paper on a baking sheet. On a lightly floured surface, roll out the orange dough to about 1/2-inch or a bit thicker. Use a small kitty face cutter (around 1 1/2 inches in diameter) to cut out as many faces as you can and transfer to the parchment paper. Push together the scraps, then roll and cut again. Brush the faces with a little cold water and stick them all together into a log 8 to 9 inches in length. Refrigerate or freeze until very firm, 1 hour in the fridge or 30 minutes in the freezer.
Once the orange log is firm, cut the teal piece of dough into 8 pieces and roll each into a snake about as long as the log. Press the snakes to flatten slightly. Stick the snakes on the log all around, covering the log. Roll the log gently on the counter to make it round (but don't put so much pressure that you smoosh the kitty faces inside). Once the log is round spread 1/2 cup or so of nonpareils on a plate or small rimmed baking sheet. Roll the log to coat in nonpareils. Wrap tightly in plastic and refrigerate or freeze again until firm. (The cookies can also be made up to this point and frozen for later use.)
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
Unwrap the dough and use a sharp knife to cut cookies just a bit more than 1/4-inch thick. Space the cookies about an inch apart on the baking sheets. Bake, rotating the trays from top to bottom once, until crisp on the edges, 10 to 12 minutes. Cool.