Make the cake batter: Preheat the oven to 350°F (175°C). Grease and flour three 8-inch cake pans. In one bowl, sift together the flour, sugar, baking soda, salt, and cocoa powder. In another, whisk the oil, buttermilk, eggs, green food coloring, vinegar, and vanilla. Gradually mix the dry ingredients into the wet until just combined.
Bake the cake: Divide the batter evenly between the pans and bake for 25–30 minutes, until a toothpick inserted in the center comes out clean. Let cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.
Make the frosting: Beat the butter and cream cheese until light and fluffy. Gradually mix in the powdered sugar, then add the vanilla extract and beat until smooth.
Assemble and frost: Place one cake layer on a serving plate and spread with frosting. Repeat with the second and third layers, then frost the top and sides. Garnish with green sprinkles, gold dust, or chocolate shavings.