To start off, pour 1 ½ cups of your chosen champagne into a small saucepan set over medium-high heat. Allow it to come to a simmer, stirring occasionally as it begins to bubble. Keep simmering until it reduces down to approximately ¼ to ⅓ cup (60-80 mL). This reduction process usually takes around 10-15 minutes. Once reduced, transfer it to a heatproof container and let it cool completely while you prepare the cookie dough.

In a large mixing bowl, place your softened unsalted butter and granulated sugar. Using an electric mixer, beat these two ingredients together until they achieve a fluffy, creamy consistency. This will take approximately 3 minutes. Remember to occasionally scrape down the sides of the bowl; we want every ounce of that buttery goodness incorporated!

Next, add the large egg yolk, vanilla extract, and sea salt to the butter-sugar mixture. Give it a quick mix to combine everything thoroughly, ensuring you scrape the sides and bottom of the bowl so no sweet surprises get left behind.

With the mixer set to low, gradually add the all-purpose flour and cornstarch to the bowl. Go slow here to avoid a flour explosion in your kitchen! Mix just until the flour is incorporated; over-mixing will lead to a stickier dough than intended.

Once your dough is formed, transfer it to a clean, floured surface. Shape the dough into a disk about 1-inch thick, wrap it in plastic wrap, and refrigerate for a minimum of 15 minutes; up to 5 days is also fine if you want to prepare ahead.

After chilling the dough, preheat your oven to 350°F (175°C). Lightly flour your work surface again and roll out the chilled dough to about ¼-inch thickness. If the dough feels too tacky, pop it back in the fridge for a little longer or dust more flour on top. Now, grab your star-shaped cookie cutter and start cutting out cookies. Gather the scraps, re-roll them, and cut out more cookies until all dough is used.

Line a baking sheet with parchment paper, and arrange the cookie shapes on it. Bake these little beauties for about 10-12 minutes, keeping an eye on them. You want the edges to turn a light golden brown—the rest should be set but still soft.

After baking, let the cookies cool on the sheet for 5-10 minutes. Then, carefully transfer them to a cooling rack to cool completely before adding the icing.

While the cookies cool, prepare your icing. In a mixing bowl, whisk together the powdered sugar, melted butter, and about 2-3 tablespoons of the reduced champagne. If it needs to be thinner, add whole milk gradually until you achieve a ribbon-like consistency that holds its shape momentarily before dissolving back into the bowl.

Now the fun part! Grab a cookie, hold it by the base, and dip it into the champagne icing. Once it’s coated to your liking, return it to the cooling rack and sprinkle with colorful sugar for a festive touch. Allow the frosting to set completely, which typically takes about 1 to 3 hours, but patience is key!