Heat your oven to 350°F. Line a baking sheet with parchment paper.
Pour flour, cinnamon, ginger, cloves, nutmeg, baking soda, and salt in a medium bowl. Stir to combine. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat vegan butter and sugar on medium-high until light and fluffy (about 2 minutes). Beat in the flax egg until well combined.
Reduce speed to low. Gradually add flour mixture to butter. Continue beating until combined.
Continue with the mixer on low and add the molasses, plant-based milk, and apple cider vinegar.
Roll the batter by quarter cup into balls and place on a prepared baking sheet, about 1.5" apart. Bake about 10 to 12 minutes, until edges are golden brown.
Remove from oven and cool slightly before transferring to a wire rack to cool completely.
Prepare the Vegan Cream Cheese frosting. Clean out the bowl and the paddle attachment from above. On medium-high beat vegan butter and vegan cream cheese until fluffy, about 2 to 3 minutes.
Reduce speed to low and gradually add powdered sugar until it's all incorporated. Add ground nutmeg.
Increase speed to medium-high until light and fluffy, 1 to 2 minutes.
Assemble the whoopie pies by placing a dollop of cream cheese frosting on the bottom side of one of the cookies, use a butter knife to spread out to edges. Then top with another cookie. Repeat until you run out of cookies!