Preheat the oven to 180°C. Line an 8" springform pan with baking paper from the bottom. I usually put butter and flour on the sides. Place the sugar, eggs, and vanilla in a large bowl and beat with a mixer until light and fluffy.
Sift the flour with the baking powder and add to the mixture in the bowl a little at a time along with the softened butter. Continue to mix until completely blended, then stir in the yogurt. In a food processor, process the whole orange until it is almost pureed. Add this orange to the cake mixture and stir until evenly combined, then put the batter into the prepared tin.
Bake for 40 to 45 minutes (depending on your oven), but test with a cake tester or skewer to make sure the orange cake is done before removing from the oven. Allow to cool for about 15 minutes, then remove the side of the springform pan.
Prepare the glaze by melting the sugar in the orange juice and simmer for a few minutes, just until the liquid has a syrupy consistency. Spoon and brush over the top of the cake and allow to cool completely before cutting.
