Preheat oven to 325 degrees (F). Line a large baking sheet with parchment paper or a non-stick silicon baking mat; set aside.
In a large bowl, cream butter and sugars until light and fluffy. Add the egg; beat well. Stir in molasses and vanilla; mix well.
In a medium sized mixing bowl combine flour, ginger, cinnamon, nutmeg, cloves, baking soda, and salt; mix well to combine. Gradually add dry mixture to wet mixture; stir until just combined.
Drop cookie dough by tablespoonfuls, leaving 2 inches between each ball.
Bake for 13-15 minutes or until cookies spring back when touched lightly. Allow cookies to cool a few minutes on the baking sheet, then transfer to a wire rack and cool completely.
For the eggnog frosting:
In a large saucepan bring the brown sugar, eggnog and butter to a boil; cook and stir for 2 minutes, stirring occasionally. Remove from the heat and cool for 5 minutes.
Add confectioners' sugar, vanilla and salt; mix well. Frost cookies, then add sprinkles (if using).
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