Preheat the oven to 350°F (177°C)
Line a loaf pan with parchment paper.
Whisk the flour, baking powder and salt together.
Using an electric mixer, cream the butter and sugar together on high until very light and fluffy, about two minutes.
Set the mixer on medium/low and mix in the eggs, one per time, until fully incorporated.
Set the mixer on medium and blend in the lemon zest and juice, yogurt and vanilla.
Add the flour mixture, one third at a time, and beat on medium/high until fully combined.
Scrape down the sides and bottom of the bowl as necessary.
Once the ingredients are fully incorporated, pour the batter into the parchment paper lined loaf pan.
Bake the cake for 45 minutes to an hour until a toothpick comes out mostly clean.
Let the cake cool for close to an hour then remove it from the loaf pan.
While the cake is cooling prepare the lemon glaze by whisking the powdered sugar, lemon juice and milk together until smooth and creamy.
While the cake is still slightly warm drizzle the lemon glaze on top of it.
The cake can be frozen; if you do, wait to ice the cake once it has defrosted.