Preheat the oven to 350F. Grease and line a loaf pan with parchment paper. Leave some parchment hanging over two sides of the pan to make it easy to lift the cake out when it is done.
In a large bowl add sugar. Using a fine grater, zest the 3 clementines into the sugar. Set the clementines aside for juicing for the glaze later.
Whisk the zest with the sugar until it has the texture of slightly damp sand and is fragrant.
In another bowl, whisk together the flour, baking powder, and salt.
Add the yogurt to the sugar and clementine zest mixture and whisk it together well. Add the eggs and whisk vigorously for about a 30 seconds. Stir in the vanilla.
Using a large spoon or spatula, stir the flour mixture into the wet ingredients until it is combined. Pour in the olive oil and fold it in until it is fully incorporated and the batter is shiny and smooth.
Pour batter into prepared pan and bake at 350F for 50-55 minutes or a toothpick comes out clean with the cake is tested.
While it bakes, prepare the glaze. In a small saucepan add the honey and juice the three clementines into the pot. Bring the juice and honey to a boil for about 30 seconds. Turn off the heat and set it aside until the cake is done.
When the cake is fully baked, and just out of the oven, brush all the glaze on the hot cake with a pastry brush while it is still in the pan. Try to brush glaze over the whole top and particularly in the crack on top
Removed the freshly glazed cake from the pan and let it cool on a rack.