Combine the flour, baking powder, salt, nutmeg, and cinnamon in a medium mixing bowl and set aside.
In the bowl of a stand mixer cream sugar and butter until fluffy. (You can also use a large mixing bowl and a hand mixer.)
Add egg yolks, eggnog, rum, and vanilla extract. Beat at medium speed with a mixer until smooth.
Slowly add flour mixture. and beat at low speed until combined. Do not over mix!
Roll dough into 1-inch balls and place on a baking sheet lined with a silicone mat or parchment paper. Space cookies about two inches apart.
Bake for 10-13 or until edges are golden. (Baking time may vary a little by oven. You made an extra minute or two.)
While cookies are baking, make your eggnog glaze. Whisk together powdered sugar and eggnog. Add the eggnog slowly until you reach a drizzle consistency, about 4-5 tablespoons.
Cool cookies on wire cooling rack and drizzle with glaze once cooled completely. Store in an airtight container.
Notes
The alcohol in the rum will bake off while the cookies are in the oven. If you prefer, you can substitute 1/2 teaspoon rum extract instead.