Preheat oven 350F, with rack on lower middle position. Lightly grease 9x5" loaf pan and set aside.
In a bowl, hand-whisk together the yogurt, sugar, eggs, lemon zest, vanilla, and olive oil. Whisk until well incorporated.
In a separate bowl, hand-whisk together the flour, baking powder, and salt. Using a rubber spatula or wooden spoon, gently fold flour mixture together with the yogurt mixture until most lumps are gone - a few small lumps are fine.
Use a rubber spatula to transfer batter into greased loaf pan and bake 60-70 min. or until toothpick inserted in center comes out almost clean, with a few tender crumbs attached. Let cake cool in pan slightly at room temp, while you make the lemon syrup.
Combine the 2 ingredients for Lemon Syrup into a saucepan. Stir over medium heat until completely dissolved.
Use a sharp knife to loosen warm cake from pan and carefully flip cake over onto a serving platter. Using a bamboo skewer or toothpick, poke holes throughout top of cake. Brush lemon syrup over the cake until it's soaked into the cake. Let cake cool.
Make the lemon glaze by combining the 3 ingredients for Lemon Glaze in a small bowl and stirring until it becomes a thick-drizzle consistency. Drizzle glaze over cooled cake. Glaze will firm up in 5 minutes. Slice and serve.
Notes
This cake is delicious as leftovers. Keep in an airtight container at room temp 1-2 days. It can also be frozen, in airtight container, for several weeks.
Always use freshly grated lemon zest for the best flavor. Avoid using the white pith of the lemon, as it can be bitter.
Don't rush the mixing process. Gently fold the dry ingredients into the wet ingredients until just combined. Over-mixing can make the cake tough.
Poking holes in the cake before adding the lemon syrup allows it to soak in and infuse the cake with even more lemony goodness.
Let the cake cool completely before adding the lemon glaze. This will prevent the glaze from melting and will give your cake a beautiful, glossy finish.
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