Preheat the oven to 350 degrees F. Spray an 8” springform pan with baking spray and then dust the pan with flour. You want the sides of the pan to be well greased and floured.
Add the sugar and eggs to the bowl of a stand mixer fitted with a paddle attachment. Beat the eggs until they are light and fluffy.
3 eggs, 1 1/4 cup sugar
Sift the flour and baking powder into the bowl with the eggs and beat slowly into a thick batter.
1 3/4 cup flour, 1 Tablespoon baking powder
Add the softened butter to the bowl and mix again.
5 Tablespoons butter, softened
Wash and slice your orange, keeping the peel on but removing any seeds. Place the orange slices in a food processor or blender along with the yogurt and vanilla extract. Blend until the orange is smooth. A few pieces are okay but you want to get it as smooth as possible.
1 large orange, washed, 5 Tablespoons plain Greek yogurt, 2 teaspoons vanilla extract
Add the orange mix into the mixing bowl and blend again.
Pour the orange cake batter into the prepared springform pan. Bake the cake for one hour. Test the cake to see if it is done by sticking a toothpick in the center. It should come out of the cake cleanly, with no stick batter on it.
Let the orange cake cool in the pan for about 20 minutes.
While the cake is cooling, whisk together all the ingredients for the glaze.
1/2 cup orange juice, 1/3 cup powdered sugar, 1/4 teaspoon vanilla extract
Remove the sides of the springform pan.
Brush the glaze over the top of the cake, covering it completely and letting some of the glaze drip down the sides. The cake will absorb most of the glaze right away, soaking up all that sweet, orange flavor.
Cut the cake into slices and enjoy while warm.