Preheat your oven to 325°F and use butter or cooking spray to grease a large loaf pan.
In a large bowl, using a hand- or stand mixer, beat the eggs and sugar together until the mixture is pale and thick. This may take 3-4 minutes. Add the Greek yogurt and orange zest. Beat again to combine.
Slowly add the olive oil in a steady stream while the mixer remains on medium speed and continue until the batter is well combined. Set this mixture aside.
In a separate bowl, combine the flour, baking soda, baking powder, and salt. Add this to the wet ingredients and mix gently until just combined.
Pour the batter into your prepared loaf pan and bake for 40-50 minutes or until an inserted toothpick comes out clean. Let it cool for 15-20 minutes, remove from the pan and drizzle the vanilla glaze on top. Serve and enjoy!
Vanilla Glaze
To make the vanilla glaze, in a small bowl, add the icing sugar, milk and vanilla extract. Using a whisk, mix this together until smooth. If you prefer a thinner consistency, add more milk 1 tsp at a time. If you want a thicker glaze, add more icing sugar, 1 tbsp at a time. Once your desired consistency is achieved, set it aside.
Notes
Eggs
If you want to make this loaf vegan, you can try using flax eggs instead.
Greek yogurt
I recommend using plain Greek yogurt, since we get the sweetness from the sugar. However, if you prefer to use a vanilla or even a lemon Greek yogurt, they would work nicely too.
If you want to make this loaf vegan, you can opt for a plant-based neutral-tasting yogurt.
Oil
I have used both vegetable oil and a mild olive oil in this recipe and they both work. If you do opt for olive oil, please ensure it is a mild flavour so that it doesn't overpower the other components.
Flour
If you want to make this gluten-free loaf, I recommend Bob's Red Mill 1-to-1 gluten-free flour. Use the same amount that is called for in this recipe.
Orange zest
If you don't have a zester, you can use the finest side of your box grater.