Whisk all-purpose flour, icing sugar, and salt in a large mixing bowl.
To this, add vegan butter cubes and vanilla extract.
Working with your finger, mix the butter with the flour mixture and slowly work until everything comes together into a smooth dough.
Initially, you might feel it's not coming together, but the dough will be formed as soon as the butter softens. It will take a minute or a couple of minutes.
Once smooth and soft dough is formed, stop kneading. Avoid over-kneading, as the butter will start warming, making the dough sticky.
The dough should be soft and hold its shape, but not sticky or crumbly. Cover the dough tightly and chill in the refrigerator for at least 30 minutes.
Preheat the oven to 325°F (160°C). Line the cookie sheet with a silicone mat or parchment paper.
Place a sheet of parchment paper on a clean surface and sprinkle with a little flour. Then, place the dough ball in the middle of the parchment paper.
Use another piece of parchment paper for the top, and roll the dough to about ½ inch thick.
Using the circular cookie cutter, cut out the cookie dough into circles.
Instead of a circular cookie cutter, you can use your favorite one to shape the cookies.
Gather the scraps, roll them again into a ½-inch thick disc, and make more cookie dough circles.
Carefully transfer them to the prepared cookie sheet and place them at least 1 inch apart.
Bake the cookies for 18-20 minutes or until they are dry to the touch and lightly golden around the edges.
Remove the cookies from the oven and sprinkle generously with cane or granulated sugar while they are still warm.
Then, transfer them to wire racks and allow them to cool completely.