Mix flour, cacao powder, powdered sugar, vanilla extract, and lemon zest in the bowl of a stand mixer.
Add the dairy-free butter and milk. Mix, with a flat beater attached, until you have a smooth dough. → Feel free to mix the dough by hand if you don't have a stand or hand mixer.
Form it into a ball or disc, cover with plastic wrap, and refrigerate for 30 minutes. → The dough can be refrigerated for up to two days. If so, let it sit for 15 minutes at room temperature before rolling it out.
Preheat your oven to 355°F (180°C).
Place the dough on a floured surface and roll it out, using a rolling pin, to about ¼-inch (½ cm) thickness.
Using a linzer cookie cutter, cut the dough into shapes. Re-roll the remaining dough and continue cutting until all dough is used. → Make sure that you have an equal amount of bottom and top cookies.
Transfer the cookies to a parchment paper-lined baking sheet and bake for 8 minutes in the preheated oven.
Remove from the oven, allow cookies to cool for 5 minutes on the baking sheet, and then transfer to a cooling rack to cool completely.
Sprinkle the tops with powdered sugar (optional) and spread ½ teaspoon of jam on the bottoms. Place the tops on the bottoms, and you are done!