Preheat the oven to 350°F/180°C and line an 8x8-inch (20x20-cm) pan with parchment paper and lightly spray with oil. Make sure the oven rack is set to the middle of the oven.
Make the vegan buttermilk. In a large bowl, combine the plant based milk of choice with the apple cider vinegar. Give this a good whisk, then set aside for 5 minutes.
Whisk the wet ingredients. Into the same bowl with the buttermilk, add the remaining wet ingredients of brown sugar, molasses, applesauce, oil, and the vanilla. Whisk again until fully combined.
Add the dry ingredients. Now, sift in the dry ingredients right into the same bowl. Add the all purpose flour, baking powder, baking soda, all the spices, and salt. Switch to a spatula or mixing spoon, making sure to scrape all the sides and bottom of the bowl. Be gentle and don’t overmix this cake batter.
Bake. Fill the prepared pan with the cake batter. Gently press it into the corners. Bake for 25-28 minutes or until it looks set, is not sinking in the middle, and a toothpick inserted into the center of a cupcake pulls out clean. Do not open the oven after you place the cake inside for at least 23 minutes.
Cool. Remove the cake from the oven and let it cool in the hot pan for 25 minutes. Then, let it finish cooling on a wire rack until fully cooled. Don’t frost until the cake is totally cool.
To make the frosting. In a large bowl with a hand mixer, or in a stand mixer with the whisk attachment, place the vegan butter and half of the sugar. Mix on medium-high speed until the frosting begins to form, making a creamy and smooth frosting. Add the remaining sugar, vanilla, salt, and any plant based milk if needed. Whisk again on high speed for 2 minutes or so until you have a light and fluffy frosting!
Frost and serve. Frost the cake with an offset spatula, or even just the back of a spoon. Sprinkle with any sprinkles, top with tiny gingerbread people, and enjoy!