Preheat oven to 350 degrees F.
Line baking sheet with parchment paper and set aside.
In large bowl, beat together butter and sugar until well combined, about 2 minutes.
Add eggs, one at a time, mixing until combined.
Add eggnog and extract, until combined.
In separate bowl, whisk together flour, baking powder, nutmeg, and salt.
Gradually add flour mixture to wet mixture.
Fold in cranberries.
Refrigerate for 30 minutes.
Separate dough in half, and form into two 1" high logs on a well floured surface. They should be oblong shaped.
Place them onto prepared baking sheet.
Bake in preheated oven for 25 minutes, until golden brown.
Remove from oven and let cool until warm enough to handle, but still warm.
Cut crosswise into ~½" slices.
Place them onto baking sheet (same one you used before) cut side down.
Bake 10 minutes, then flip to other side and bake another 8-10 minutes.
Let cool completely before glazing.