Preheat oven to 350. Line a baking sheet with parchment paper and set aside.
In a mixing bowl, combine butter, sugar, salt, vanilla, rum extract, baking powder, and nutmeg until creamy. Beat in eggs one at a time. Carefully stir in flour, beating until mixture is smooth.
Transfer your dough onto your baking sheet and shape dough in a log about 14 inches long and about 2 inches wide.
Bake for 25 minutes. Remove from the oven and let stand for about 15-25 minutes. 5 minutes before cutting, gently sprinkle with water, taking care to reach all sides of the biscotti.
Reduce oven temperature to 325. Wait another 5 minutes and slice biscotti into ¾ inch slices. Stand biscotti upright and bake for 25 more minutes. Remove and let cool on baking sheet.
When biscotti have cooled, lay cookies on one side. Drizzle with glaze.
To prepare the glaze, whisk together the butter and powdered sugar. Add eggnog and whisk until mixture is desired consistency.
Once the glaze has set, store cookies in an airtight container.