Preheat the oven to 350℉ and grease an 8x4-inch loaf pan, spray with baking spray with flour or line with parchment.
In a large bowl, whisk together flour, baking soda, and salt.
In a separate bowl, combine sugar and orange zest, rubbing the zest into the sugar with your fingertips-- this helps enhance the orange flavor. Add the oil, melted butter, eggs, orange juice, and vanilla, and whisk until combined.
Pour the wet ingredients into the flour mixture and whisk together until the flour is incorporated, but be careful not to overmix. Pour the batter into the prepared loaf pan.
Bake for 60-70 minutes or until a toothpick inserted into the center comes out mostly clean. If needed, tent a piece of foil over the cake toward the end of baking if it browns too quickly. Let the cake cool in the pan for 15 minutes before removing from the pan to cool completely on a wire rack.
For the icing:
Whisk together powdered sugar, zest, and juice in a small bowl until smooth. Drizzle over the cooled cake and let it stand until set. Store the cake in an airtight container for up to 5 days.