Preheat oven to 325 degrees (F). Line a large baking sheet with parchment paper or a non-stick silicon baking mat; set aside.: The air in the oven should smell neutral and warm when ready, and the parchment will prevent sticking and promote even browning. I always let the oven reach temperature for at least 10 minutes so the first tray bakes predictably. Listen for a quiet hum from the preheating element and watch the temperature dial or digital readout for stability. If you place cookies into a slightly cool oven, they will spread less and bake longer, so patience here avoids flat or underbaked centers.
In a large bowl, cream butter and sugars until light and fluffy. Add the egg; beat well. Stir in molasses and vanilla; mix well.: You will notice the mixture go from gritty to smooth, with the color deepening as the molasses blends in. The sound changes too, from a faint scraping to a steady, smoother whir if using a mixer. This step traps air in the butter , creating lift and a tender crumb. If you overbeat, the dough can become too airy and collapse during baking, so stop when it looks pale and holds a soft ribbon when lifted with the paddle.
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.: The dry ingredients should smell fragrant, a compact, spicy bouquet that promises warmth. Whisking helps distribute the baking soda evenly so pockets of leavening do not create odd rises. If you skip thorough mixing, you might bite into unevenly spiced cookies or encounter tiny salty bursts. Sifting is optional but useful if your flour is clumpy.
Drop cookie dough by tablespoonfuls, leaving 2 inches between each ball.: The dough will change from glossy to a thicker, slightly sticky mass, and you will see stripes disappear as flour incorporates. Work slowly to avoid overworking gluten, which makes cookies tough. Stop mixing as soon as streaks vanish; the dough should be pliable and hold shape. If it feels dry, a tablespoon of eggnog can help, but avoid adding too much or the cookies will spread too thin.
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.: You will feel slightly tacky dough on your fingers that smooths into rounded mounds when scooped. Leaving space lets the cookies expand and form those delicate crisp edges. If you crowd the sheet, cookies will merge into one another. Use a measuring spoon for consistent size so they bake evenly across batches.
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.: The kitchen will fill with a sweet, spiced perfume and the tops will look set and slightly glossy. Gently press a finger into the center for the spring back test; if it holds a slight indentation, they need a bit longer. Leaving them too long will crisp them entirely, losing chewiness. Letting them rest on the sheet first keeps them from breaking while warm, then the wire rack allows air to circulate and cool them evenly.
Add confectioners' sugar, vanilla and salt; mix well. Frost cookies, then add sprinkles (if using).: As the mixture simmers, you will smell caramelizing sugar and see tiny bubbles break the surface, a rich, toasty aroma. Boiling briefly thickens the syrup so the glaze is flavorful and not watery. Remove promptly and allow to cool so it does not melt the confectioners sugar on contact. A common error is boiling too vigorously, which can scorch the sugar and impart a bitter note.
Add confectioners' sugar, vanilla and salt; mix well. Frost cookies, then add sprinkles (if using).: The frosting should glide smooth and glossy, with a velvety sheen from the heavy cream and butter . Spread while the glaze is warm but not hot so it levels neatly, and the sprinkles will adhere. If the frosting is too thin, add a bit more confectioners sugar ; if too thick, thin with a teaspoon of eggnog . Don't frost hot cookies or the glaze will run and create a thin, uneven coating.