Preheat oven to 350 degrees F. Grease a 9x5 inch loaf pan. Set aside. Tip: if desired, line the pan with parchment paper with overhang on both sides of the pan (the long sides) to make it easier to pull out the cake later.
Whisk the dry ingredients: In a bowl, whisk the flour, baking powder, and salt. Set aside.
Cream the butter with the sugar: In the bowl of a stand mixer with the paddle or whisk attachment, beat the softened butter over medium-high speed until light and smooth for 1 to 2 minutes, scraping the sides of the bowl as needed. Add the granulated sugar and beat over medium-high speed until light and fluffy, about 2 minutes, scraping the sides of the bowl.
Reduce to medium speed, and add the eggs, one by one, until fully incorporated.
Add the Greek yogurt, lemon zest, and vanilla. Mix over medium speed. Add the lemon juice and mix a few more times. Note: It may look curdled, that’s normal. The batter will come together once you add the dry ingredients.
On medium speed, mix in the dry ingredients into the mixture gradually, until combined and no pockets of flour remain. Do not overmix. The batter will be thick. Tip: Sometimes flour gets stuck in the bowl or in the batter. Just fold the batter a few times using a rubber spatula at the end to make sure it’s all combined.
Transfer the batter to the prepared loaf pan.
Bake in the middle rack for 55 to 60 minutes, or until a toothpick inserted in the middle comes out clean. A few moist crumbs are fine. Try not to open the oven while it's baking, otherwise it may collapse in the center. Note: If the top is browning too fast, tent with foil, usually after 45 minutes into the baking time.
Remove from the oven and let it cool in the pan for about 1 hour, over a wire rack. Then carefully remove the cake from the pan and let it cool completely for another 2 hours or so.
Make the lemon glaze: In a medium bowl, add the confectioners sugar. Add the lemon juice and the heavy cream gradually, one tablespoon at a time, whisking until you get the consistency you want. I like my glaze thick, so I made sure to add the liquid little by little until it was just about right. If you want it thinner, just continue adding more heavy cream.
Drizzle or pour over the pound cooled cake. Garnish with lemon zest if desired. Slice and serve. Enjoy!