Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, and vanilla extract. Mix on low until combined, then speed the mixer up to speed 4 and mix for about 5 minutes until the butter has lightened in color and is fluffy.
Next, add the sourdough discard and dry ingredients: flour, allspice, and cloves. Mix together until combined into a smooth dough.
Add the turbinado sugar to a small bowl.
Using your hands, form the dough into 30 small balls and roll each dough ball in the turbinado sugar.
Place the dough on the prepared parchment-lined baking sheet and press your thumb into the center to create an indention. Using a small spoon, fill the indent with jam.
Bake for 19 to 22 minutes, or until lightly browned on the bottom. Let cool completely on the cookie sheets.
Store in a cool, dry place for up to 3 days.