Preheat oven to 350F Grease and flour 3 9-inch baking pans, and then line the bottoms with a round of parchment paper. Note: the parchment paper is important because the cakes can stick without it.
Whisk the flour, baking powder, and salt together. Set aside.
Put the sugar in a food processor, along with the zest of one lemon. Note: you don't want the peel of the lemon, just the outer zest. Use a serrated vegetable peeler for best results and just peel off the yellow part, leaving the bitter white behind. Process the sugar and zest together until the zest is completely incorporated, and the sugar is moist and pale yellow.
Cream the soft butter and the lemon sugar together in a stand mixer for 3 minutes, scraping down the sides of the bowl as needed.
Beat in the eggs, one at a time, beating between each addition, scraping down the sides of the bowl to get everything incorporated. Add the lemon paste.
Reduce the mixer to low speed and add the flour, mixing just until barely combined, then add the buttermilk and lemon juice. Mix until everything has come together, but don't over-mix.
Divide the batter equally between the 3 pans and spread out evenly.
Bake for about 23-25 minutes, or just until risen and a toothpick inserted in the center comes out without wet batter clinging to it. Don't over bake these layers ~ they're thin and will cook quickly.
Let the cakes cool in the pans on a rack. When they are cool, carefully flip them over and remove the parchment paper.
To make the frosting cream the butter and sugar, gradually adding enough lemon juice to make a spreadable frosting. You may need a little more or a little less than the amount stated. Add the poppy seeds and beat until the frosting is smooth and creamy. Add more lemon juice to make it thinner, or more sugar to thicken it. If you'd like a pale yellow tint to your frosting, add a drop or two of food coloring and mix in thoroughly.
Frost the cake and then garnish with the lemon slices and mint leaves.