Preheat the oven to 350ºF. Line 16-18 muffin tins with cupcake liners.

In the bowl of a mixer, beat the butter until smooth. Add the sugar and beat until light and fluffy, about 3 minutes. Add in the eggs, one at a time, beating for a full minute after each addition. Beat in the vanilla and rum extracts.

In a bowl, whisk together the flour, baking powder, salt, nutmeg and cinnamon. Add one-third of the flour mixture to the butter mixture and beat just until combined. With the mixer still running, slowly add half of the eggnog. Add in another one-third of the flour mixture, followed by the remaining eggnog, then the remaining flour, beating after each addition, scraping down the sides of the bowl as needed.

Fill each of the cups 2/3 full of the batter. Bake until a tester inserted in the center comes out clean, about 18 minutes. Let the cupcakes cool for 5 minutes, then transfer to a cooling rack to cool completely.

In the bowl of a mixer, cream the butter until very light and fluffy, several minutes. Add in the dulce de leche, vanilla extract, rum extract, nutmeg, salt and cinnamon and beat to combine. Add in the powdered sugar, 1/2 cup at a time, beating until fully incorporated. Add in the eggnog 1 teaspoon at a time until you reach your desired consistency.

Pipe the frosting onto the cooled cupcakes using your desired tip. (I used the Ateco 809 round tip.) Grate nutmeg over the tops of the cupcakes, the drizzle with dulce de leche. Refrigerate until ready to serve. Remove from the refrigerator 30 minutes before serving.