Heat oven to 350°F. Grease a 9" x 5" loaf pan and line it with parchment paper; set aside.
In a medium bowl, whisk together flour, baking powder, salt, and cardamom. Set aside.
Combine sugar and orange zest in a large bowl. Using your fingers, rub together until sugar turns yellowy-orange and you smell that citrusy goodness.
Whisk in Greek yoghurt, olive oil, eggs, and vanilla.
Add flour mixture to wet mixture, stirring just until combined.
Pour batter into prepared pan, smoothing top with an offset spatula or the back of a spoon.
Bake for 45–50 minutes or until golden brown. Cake is done when a wooden pick inserted in the centre comes out clean with only a few fluffy crumbs attached.
Transfer pan to wire rack. Allow cake to cool for 15–20 minutes, then remove from pan. Cool cake completely.
Once cake is totally cool, make the frosting. In a small bowl, beat all filling ingredients until smooth. Spread frosting over cake using an offset spatula. To add a design like ours, gently drag a fork across frosting. Top with additional orange zest, if you like.
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