Rub the powdered sugar and orange zest together in a large bowl for 30 seconds, until pale orange.
Add the soft butter, vanilla and salt. Beat for 2 minutes, until fluffy.
Add the flour and cornstarch. Mix on low speed just until the dough comes together.
Shape the dough into a log about 2 inches wide and 8 inches long. Wrap it tight.
Chill the log for at least 1 hour.
Heat the oven to 350°F (175°C). Line two baking sheets with parchment paper. Slice the log into rounds about 1/3 inch thick and place them 1 inch apart.
Bake for 12 to 14 minutes, until the edges are just golden. Cool on the sheet for 5 minutes, then move to a wire rack to cool completely.
Whisk the glaze sugar and 2 tbsp of juice until smooth, adding more juice if needed. Dip or drizzle the cooled cookies. Let the glaze set for 30 minutes.