Make the cookies: In a small saucepan, bring the champagne to a boil and reduce by half, about 5 minutes.
In a liquid measuring cup or microwave-safe bowl, microwave the heavy cream until boiling.
Pour the hot heavy cream and half of the heated champagne over the white chocolate chips in a heatproof bowl and let rest for 1 minute. Whisk until smooth. Add 4 tbsp of unsalted butter and whisk until melted and well combined. Cover and chill in the refrigerator for 2 hours.
In a large bowl, cream the remaining cup of unsalted butter and the powdered sugar with an electric hand mixer until fluffy. Add the vanilla and beat to combine.
Add the flour, 1 cup at a time, and beat until just incorporated. To the last addition, add the salt.
Add the walnuts and beat to incorporate. Using your hands, press the dough together in a ball and wrap in plastic wrap. Refrigerate the dough at least 30 minutes.
Preheat the oven to 375˚F (190˚C). Line a baking sheet with parchment paper.
Use a 2 tablespoon (1 ounce) scoop to scoop balls of cookie dough onto the prepared baking sheet. Pat each ball into a disc in your palm and fill with 1 teaspoon of the white chocolate ganache. Fold the edges in to completely cover the ganache and roll back into a ball. Once all of the cookies are filled, refrigerate for 15 minutes.
Bake the cookies for 15 minutes, until set and not too browned. Let cool.
Make the glaze: Microwave the heavy cream until boiling.
Pour the hot heavy cream and the remaining reduced champagne over the semisweet chocolate chips in a heatproof bowl and whisk until smooth.
Dip the cooled cookies in the chocolate ganache and sprinkle with edible gold dust.