Preheat the oven to 350 degrees F. Spray the sides and bottom of a 9-inch springform pan lightly with non-stick baking spray and line the bottom with parchment paper. Place the pan on a parchment-lined baking sheet.
Whisk together 1 ¾ cups all-purpose flour, 1 teaspoon baking soda, 1 ½ teaspoons baking powder, and ½ teaspoon salt in a small bowl.
Blend 4 whole clementines (11 ounces) and 2 teaspoons vanilla extract in a blender or food processor until a smooth paste is formed. Set aside.
In a large bowl, cream together 2 large eggs, room temperature and 1 cup granulated sugar using a hand mixer until light and fluffy. Slowly add ½ cup olive oil and beat for 3 more minutes. Pour in the clementine paste and beat until incorporated.
Add the dry ingredients to the wet ingredients and beat together. Don’t overmix.
Pour the batter into the springform pan and bake for 20-30 minutes or until golden brown and a toothpick inserted in the center comes out clean.
Let the cake cool on a baking tray for about 30 minutes or until the sides of the cake pull away from the edge slightly. Transfer the cake to a wire rack and let it cool completely, about one hour.
Glaze
Mix 2 cups powdered sugar, sifted and 2-3 tablespoons clementine juice in a measuring cup or bowl. Whisk in 1 tablespoon of yogurt. If it is too thick, add a little more juice or yogurt to thin it out.
Assembly
To remove the springform pan, run a knife around the edges of the pan to help loosen and remove the side. Use an offset spatula to gently loosen the cake from the bottom of the pan, and then remove the parchment paper and place the cake on a platter. Pour the glaze over the cake. Decorate with clementine slices.
Notes
Make sure whatever citrus you ultimately use doesn't have seeds. If they do, remember to remove them before blending them into your cake.
When you first start mixing the glaze, it will feel very thick. As you combine all the ingredients, it will thin out. It’s important to make sure it’s slightly on the thicker side so that it will adhere to the cake best.
The cake must be completely cooled before glazing, or it will melt into parts of the cake and not adhere.