For the Eggnog Biscotti:
Preheat oven to 325°F. Line baking sheet with parchment paper, set aside.
In large bowl of stand mixer fitted with paddle attachment, combine flour, sugar, baking powder, salt, nutmeg and cinnamon until evenly mixed together. Add butter and beat on low speed until mixture resembles coarse crumbs. Increase speed to medium and add eggs, one at a time, mixing well after each addition. Stir in rum and hazelnuts and beat until well combined.
Turn dough out onto lightly floured work surface, and knead by hand until dough comes together. Divide in half and shape each half into 14-inch log. Place logs about 3-inches apart on prepared baking sheet and then flatten out to about 2-inches wide. Bake until set, and very lightly golden brown around edges, about 20 to 25 minutes. Remove from oven and let cool on rack 10 minutes.
Reduce oven temperature to 275°F. Transfer dough logs to cutting board and slice on an angle into 3/4-inch thick slices. Return slices to baking sheet, in single layer, cut side down. Bake 13 minutes, flip over, and return to oven to bake 12 to 13 minutes more or until lightly golden brown. Remove from oven and let cool completely.
For the Glaze:
In small bowl, whisk together powdered sugar, rum and enough milk until desired consistency is reached. Drizzle glaze over cooled biscotti and let set before serving. Can be kept in airtight container at room temperature for up to 3 days.