Preheat the oven to 350F (175C). Line the bottom and sides of an 8-inch (20cm) springform pan with parchment paper.
Grease the bottom of the pan with melted butter and sprinkle brown sugar evenly over it.
Arrange the orange slices over the sugar in an overlapping spiral, ensuring the bottom is fully covered. Set aside.
In a mixing bowl, beat the butter, vegetable oil, sugar, and vanilla extract with a hand mixer until pale and fluffy.
Add the eggs and beat until fully combined.
In a separate bowl, whisk together the flour, baking powder, and salt.
Add half of the dry ingredients to the wet mixture and mix just until incorporated.
Pour in the milk and mix to combine.
Add the remaining dry ingredients and mix until the batter is smooth.
Pour the batter over the orange slices. Swirl a toothpick through the batter to release large air bubbles, being careful not to disturb the oranges.
Bake for about 40 minutes or until a toothpick inserted in the center comes out clean.
Let the cake rest in the pan for 10 minutes.
Remove the springform ring and peel away the parchment from the sides. Place a serving plate over the cake, then invert it in one quick motion. Lift off the bottom of the pan and gently peel away the parchment.
For the optional syrup, heat the sugar and water in a saucepan until the sugar dissolves and the mixture boils. Brush over the orange slices before serving.