Make the cake: Preheat the oven to 350°F. Spray an 8-inch cake pan with nonstick baker’s coating, or rub with softened butter and dust with flour, shaking off the excess.

Whisk together the dry ingredients: flour, baking powder, baking soda, and salt.

In the bowl of a standing mixer fitted with the paddle attachment, beat the egg yolks with ½ cup of the sugar until light and fluffy, 5 to 6 minutes.

In a bowl or quart-size measuring cup, whisk together the milk, olive oil, and orange zest. Add to the egg yolk mixture and beat to combine. Add the flour mixture, beating just long enough to combine.

In the clean and greaseless bowl of a standing mixer fitted with the whisk attachment, beat the egg whites until fluffy. Add the remaining ¾ cup sugar and continue beating until the whites are firm and glossy, 4 to 5 minutes. Fold the meringue into the batter one-third at a time, so as not to deflate the meringue.

Pour the batter into prepared cake pan and bake for 45 minutes, or until the cake begins to come away from the sides of the pan and a toothpick or skewer stuck in the center comes out clean. Remove the cake from the oven, let it cool on a wire rack until it is warm to the touch, then invert onto a serving platter and cool completely.

Meanwhile, make the syrup: Using a swivel-blade peeler, remove the rind from both oranges in long, thin strips with a minimum of white pith. Cut the strips crosswise into thin slices. Section both oranges and reserve. Bring a small saucepan of water to a boil, add the orange zest strips and bring the liquid back to a boil over high heat. Boil 1 minute, then drain.

In a medium saucepan, combine the orange juice, sugar, and the blanched orange zest strips. Bring to a boil, reduce the heat, and simmer for 15 minutes, or until the syrup is slightly thickened, skimming as necessary. Strain the syrup, reserving the orange strips. Mix the strips with ½ cup of the strained syrup and reserve. Use a toothpick to poke holes in the top of the cake and then pour the remaining syrup all over the cake.

Pour the reserved syrup with orange zest into a small saucepan. Bring to a boil and cook down until the syrup thickens and just begins to darken, about 5 minutes. While still hot, use a spatula to spread this thick glaze over the top of the cake. Arrange the reserved orange sections on top of the cake, cut into serving portions, and serve. Store covered and at room temperature up to 3 days.