Line one baking sheet with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, dark brown sugar, molasses, and vanilla extract. Mix on low until combined, then speed mixer up to medium and continue to cream the butter mixture for 5 minutes, until it is noticeably lighter in color.
Add the sourdough discard and dry ingredients: flour, Chinese five spice, baking soda, and salt in that order. Mix on low until combined into a stiff dough.
To make the topping: Add the cane sugar to a small bowl.
Using your hands, or a 1 tablespoon cookie scoop, form or scoop the dough into 24 balls and roll them in the cane sugar. Place on the prepared baking sheet.
Refrigerate the baking sheet for at least 1 hour, or you can refrigerate overnight.
Preheat the oven to 375°F. Line another baking sheet with parchment paper.
Transfer half the cookie dough balls onto the second baking sheet, and space them all at least 1-inch apart.
Bake for 10 to 12 minutes, or until the cookies look puffed and dry around the edges. Allow to cool completely on the baking sheets.
Store in an airtight container for up to 7 days.