Preheat the oven to 350 F. Prepare a 9-inch cake pan by lining the bottom with parchment paper.
In a small bowl or glass measuring cup whisk together the almond milk or soy milk and apple cider vinegar. Set aside for 10 minutes to curdle and become dairy-free buttermilk.
In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
In a medium bowl whisk together the sugar, curdled almond milk, olive oil, orange juice, orange zest, vanilla extract, and almond extract. Make sure that the sugar has dissolved.
Pour the wet ingredients into the dry ingredients. Fold together until combined.
Pour the batter into the prepared cake pan. Smooth out the top with a spatula to even out the batter.
Place on the middle rack of the preheated oven. Bake for 28-30 minutes or until golden brown on top and a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 10 minutes.
While the cake is baking make the orange syrup. Whisk together 2 tablespoons of orange juice, and 2 tablespoons of orange juice. Make sure the sugar is dissolved.
After the cake has cooled for 10 minutes, use a skewer to poke holes around the cake. Pour the orange syrup on top of the cake and into the holes.
Run a knife around the edge of the cake. Carefully remove the cake from the pan. Allow the cake to cool completely. Dust with powdered sugar, and garnish with orange slices. Store covered at room temperature for up to 3 days, or in the refrigerator for up to 5 days.