Heat oven to 350°F. Line 2 baking sheets with parchment paper.
In a large bowl, beat powdered sugar and butter until light and fluffy. Scrape the sides of the bowl. Add the egg, orange zest, vanilla, salt, and prosecco. Beat until well combined. Add flour and mix until combined.
Prepare a piping bag with a star tip. Fill the bag with the dough and pipe it in a circular motion onto the prepared pans.
Bake for 10-12 minutes or until lightly browned on the edges. Cool completely.
While the cookies are baking, prepare the icing by mixing all the ingredients together until smooth.
When the cookies are completely cool, drizzle the icing on top.