Preheat the oven to 350 degrees Fahrenheit. Grease one 9-inch cake pan with olive oil or line with parchment paper.
Juice and zest the navel orange. Set aside.
Whisk together the flour, sugar, baking soda, salt, cinnamon, nutmeg, cloves, and orange zest in a medium mixing bowl.
In a separate bowl, whisk together the non-dairy milk, olive oil, two tablespoons of orange juice, apple cider vinegar, and vanilla extract.
Pour the liquid ingredients into the dry ingredients. Stir until just combined.
Pour the cake batter into the 9-inch cake pan, spreading into an even layer. Bake at 350F for 25-30 minutes, or until the cake is domed and a toothpick inserted in the center comes out clean. The cake should be golden and pulling away from the edges of the pan.
Let rest for 10 minutes before turning out onto a cooling rack. Once cooled, top with powdered sugar using either a sifter or a fine mesh sieve.
Notes
Sugar: Granulated sugar is not always vegan. Choose organic granulated sugar or one labeled as vegan.
Milk: I use soy milk for most vegan baking. Oat or almond milk also works. I recommend unsweetened, unflavored milk.
Olive oil: I like California Olive Ranch brand extra virgin olive oil. I recommend using an extra virgin olive oil with a flavor that you enjoy. You don't need anything too fancy, but don't choose the cheapest oil either. Light olive oil is too neutral to come through in this cake, whereas rich olive oil can be too bold.