Preheat your oven to 350°.
Grease the bottom and sides of a 10 inch round cake pan. Line the bottom of the pan with parchment.
Combine flour, sugar, baking powder, baking soda, salt, and chopped rosemary in a medium bowl, stirring to combine.
Using a large spoon, make a well in the center of the dry mix. Add oil, oat milk, orange juice, and orange zest, stirring until smooth.
Pour the batter into the prepared pan, immediately placing it in the oven so the orange juice and baking soda don't start to react.
Bake the cake for 45-50 minutes. It should be golden brown on the edges. Insert a toothpick in the center to be sure the cake is fully baked. It should come out clean.
Let the cake cool while in the pan for at least 30 minutes before you move it to a wire cooling rack.
To make the icing, combine the orange juice with powdered sugar until it's smooth and pourable.
Beginning at the top, pour the icing over the cake. It may help to tilt the cake to get an even spread of the icing around the top. The icing will drip down and cover most of the sides of the cake.
Let the cake cool and set completely before cutting. This recipe serves 8-10 slices.