Preheat oven to 350ºF. In a medium bowl, mix salt, baking powder and flour. Set aside.
With a stand mixer or hand mixer, cream together the sugar and butter. Add one egg at a time, vanilla and lemon extract, lemon juice, milk and lemon zest. Next, slowly add in the flour mix. Do not over mix, but it should form a thick batter, you can add an extra Tbsp or two of milk if needed to thin the batter a bit.
In a 9 inch cake pan, place parchment paper on bottom or, grease the pan properly and sprinkle just a little flour around it to help prevent sticking. Using a spatula, add the batter to the cake pan. You will need a little patience, just push the batter around to the edges and make sure it is evenly spread and mostly smooth on top.
Put the cake pan in the oven, cook for about 22-25 minutes. Check on it at 25 minutes with a toothpick in the center. If it comes out clean it is finished. Allow the cake to cool for about 10-15 minutes. Meanwhile while it's cooling, mix the icing together. Set aside.
Once the cake has cooled, take it out of the cake pan carefully. Set it on a cutting board. Dust with powdered sugar and leftover lemon zest. Drizzle the icing over the top, don't be shy. Slice and enjoy!