For the Cake:
1/2 Cup Olive Oil, plus more for brushing (try the Blood Orange Olive Oil – it’s perfect for this cake!)
1 Cup all-purpose flour
1/2 Cup semolina flour
1 1/2 tsp baking powder
1 tsp Ground Cardamom
1/2 tsp Kosher Salt
1/4 tsp baking soda
1/2 Cup sugar, divided
3 large eggs, separated
2/3 Cup plain whole-milk yogurt
1 1/2 tsp Grated Orange Zest
1 tsp Vanilla Extract or Vanilla Paste
Chopped unsalted pistachios, lightly toasted
9″- diameter springform pan
Make the syrup: Line a baking sheet with parchment paper. Bring sugar, orange blossom water, honey, cardamom, and 3 cups of water to a boil in a medium heavy saucepan, stirring until sugar dissolves.
Add orange slices. Reduce heat to medium-low; simmer, turning orange slices occasionally, until tender and syrup is reduced to 3 1/4 cups, about 40 minutes.
Arrange orange slices in a single layer on prepared baking sheet; remove cardamom pods and seeds. Strain syrup.
Make the Cake: Preheat oven to 350 degrees F. Brush springform pan with oil. Whisk the semolina and all-purpose flours with the next 4 ingredients in a medium bowl.
Using an electric mixer, beat 1/4 cup sugar and 1/2 cup oil in another large bowl for 1 minute. Beat in yolks, then flour mixture. Beat in yogurt, zest, and vanilla.
In yet another bowl, beat egg whites until soft peaks form using an electric mixer fitted with clean, dry beater blades [whisk attachment is preferable]. Gradually beat in remaining 1/4 cup sugar until stiff peaks form.
Fold beaten egg whites into batter just to blend, in 2 additions. Transfer to prepared pan; smooth top.
Bake cake in 350F oven until a toothpick inserted into center comes out clean, about 25 minutes.
Pierce hot cake all over with a metal skewer. Slowly drizzle 3/4 cup warm syrup all over. When syrup is absorbed, slowly pour 3/4 cup more syrup over entire cake. Reserve remaining syrup for serving.
Let cake finish cooling in pan on a wire rack. Run a thin knife around the edge of the springform pan to release cake. Carefully remove pan sides.
Arrange candied orange slices over top of cake. Sprinkle pistachios on top. Cut into wedges and serve drizzled with more orange syrup.