Place the brown sugar, vegan butter, maple syrup, and molasses into a small saucepan and set it over medium heat. Heat the mixture while stirring just until the butter and brown sugar have melted, 2 to 3 minutes. Remove the pot from heat and let it cool to room temperature.
Stir the milk and ground flaxseed together in a small bowl. Set it aside for at least 5 minutes, until the flaxseeds gel.
While the flax mixture sits, whisk the flour, cinnamon, ginger, nutmeg, cloves, cardamom, black pepper, baking soda, and salt together in a large mixing bowl.
Once the flax mixture has gelled, whisk it into the melted brown sugar mixture in the saucepan, then whisk in the anise extract.
Pour the melted brown sugar mixture into the bowl with the flour mixture and stir until a sticky dough forms.
Cover the bowl and chill the dough for 2 hours (Note 1).
Preheat the oven to 350°F and line a couple of baking sheets with parchment paper.
Roll the dough into balls, using a heaping tablespoon of dough per cookie. Place the dough balls on the prepared baking sheets, leaving at least 1 ½ inches between them.
Bake the cookies until they've puffed up and the tops feel set but don't yet look browned, 8 to 10 minutes.
Place the baking sheets on cooling racks when they come out of the oven. Let the cookies cool for at least 5 minutes on the baking sheets, then transfer them directly to the racks to finish cooling.
Once the cookies are cool, place the powdered sugar into a bowl. Roll each cookie in powdered sugar until coated.