Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the plain yogurt, fresh lemon juice, lemon zest, and vanilla extract until combined.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35-40 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
While the cake cools, prepare the lemon yogurt topping by combining the plain yogurt, powdered sugar, fresh lemon juice, and lemon zest in a small bowl. Mix until smooth.
Once the cake is completely cool, spread the lemon yogurt topping evenly over the top of the cake.
Slice and serve. Store any leftovers covered in the refrigerator.