Preheat the oven: Preheat your oven to 350°F (180°C). Lightly grease or line two large baking sheets with parchment paper.
Prepare the dough: In a large mixing bowl or the bowl of a stand mixer, cream together the vegan butter, white sugar, and brown sugar until light and fluffy. Add the molasses, vanilla extract, ginger, cinnamon, baking soda, nutmeg, cloves, and salt. Mix until smooth.
Add the oats and flour and mix well to form a dough.
Form the cookies: Scoop about 2 tablespoons of dough, roll into a ball, and place it on the prepared baking sheet. Slightly flatten each ball and space them about 2 inches apart to allow room for spreading.
Bake: Bake for 12–16 minutes, the cookies will spread and may look slightly undercooked but should be lightly golden on the bottom. Let them cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. You can either enjoy them as is, or continue to the next step to add icing.
Make the icing (optional): In a small bowl, whisk together the powdered sugar, 1 tablespoon of plant-based milk, vanilla extract, and a pinch of cinnamon and ginger. Gradually add more plant-based milk, 1 teaspoon at a time, until the icing reaches a thick yet spreadable consistency. (A thicker icing will set better, so avoid adding too much milk).
Decorate: Once cookies are completely cool, dip them into the icing or drizzle it over the tops. Optionally, add an extra sprinkle of cinnamon before the icing sets. Allow the icing to set at room temperature for a few hours.
Storage: Store the cookies in an airtight container at room temperature for up to 3 days, or refrigerate them for up to 10 days to extend their freshness. For longer storage, cookies can be frozen for up to 3 months.