Make sure the oven rack is in the middle position (unless you’ve found that another position works better in your oven for baking) and heat oven to 325 degrees. Grease and flour a 9×13″ baking dish and set aside.
Whisk together the flour, baking powder, baking soda, and salt in a medium bowl. Set aside. In a measuring cup, combine buttermilk, lemon juice, and vanilla. Set aside.
Using a stand mixer fitted with the paddle attachment, beat the white sugar and lemon zest on medium speed until moist and fragrant (about 1 minute). Remove 1/4 cup of the sugar mixture and place it in a small bowl.
Cover and set aside.
Add the softened butter to the remaining sugar mixture and beat until light and fluffy (about 2 minutes). Beat in the eggs and yolk, one at a time, until incorporated. Reduce speed to low. Add the flour mixture in 3 additions, alternating with the buttermilk mixture in 2 additions. Mix until smooth (about 30 seconds)
Scrape the batter into the reserved baking pan and smooth out the top. Bake until the cake is golden and a toothpick inserted into the center comes out clean (about 25-35 minutes). Be careful not to over bake. Transfer the pan to a wire rack and allow to cool for 10 minutes.
While the cake is cooling, whisk the glaze ingredients together until smooth. Gently spread the glaze over the cake and sprinkle evenly with the reserved sugar mixture. Allow to cool completely, at least 2 hours.