Butter a 9 x 5-inch loaf pan. Line the bottom with parchment, butter once more and dust with a tablespoon of flour. Set aside. Preheat your oven to 350 degrees F.
In a medium bowl, sift together the flour, baking powder, baking soda and salt. Next, in a medium bowl, cream together the butter and sugar until light and fluffy, about 3-4 minutes. Add the eggs, lemon zest and vanilla; and then mix until the mixture is smooth.
To the butter and sugar mixture, mix in half of the flour mixture and the buttermilk. Then, mix in the remaining flour mixture, being sure not to over mix.
In a small skillet, melt the 3 tablespoons of butter over medium heat. Whisk constantly until the butter begins to brown and then mix in the brown sugar and salt; stir until the sugar begins to bubble, about 1 minute. Turn off the heat and let stand for a few minutes to cool slightly. Pour the butter/mixture into the loaf pan, spreading it around evenly. Arrange the lemon slices atop, keeping in mind how it'll look when you flip the cake over.
Pour the batter over the lemons, and spread the batter gently so it’s nice and even. Transfer the loaf pan to the oven and bake for 35-45 minutes or until a skewer comes out clean.
Remove the cake from the oven and allow to cool for 5-10 minutes. To invert the cake, place a cooling rack on top of the loaf pan and turn both of them over; lift up the loaf pan, take off the parchment and voila! Your cake! Allow the cake to cool to room temperature before slicing.