Preheat oven to 350˚F and grease a 9x13-inch baking dish.
In a medium mixing bowl, whisk the flour with the baking powder, salt and spices. Set aside.
In a large bowl with an electric mixer, beat oil, sugar, vanilla and eggs until smooth.
In a small bowl, whisk the oat milk and lemon juice together.
Alternate adding the oat milk mixture and flour mixture to the mixer, beating until each addition has been fully incorporated. Scrape sides as need and continue until everything is combined.
Transfer batter to prepared baking dish and bake for 35 - 40 minutes, or until the cake has set (an inserted toothpick comes out clean). Remove from oven and all the cake to cool completely.
While the cake is cooling, beat the shortening and vegan cream cheese until light and fluffy and fulling combined. Add the vanilla extract, spices and oat milk, beating until combined.
Add the cornstarch, followed by 1/2 cup of powdered sugar at a time, beating until fully incorporated. Season with a pinch of coarse salt and mix until combined.
When the cake is fully cooled, spread the frosting evenly on the top, and garnish with freshly grated nutmeg (optional).