Preheat oven to 350° F (static) or 325° F (convection).
Cream butter and sugar in a large bowl, beating until light and fluffy. Slowly add eggs and yolk, one at a time, mixing to integrate. Add 2 tablespoons lemon juice and mix.
In a separate bowl, whisk together dry ingredients. Then alternately beat the dry ingredients and milk into the mixing bowl, just until combined and batter is smooth. Stir in lemon zest and poppy seeds, if adding.
Oil one 9×13 pan lightly. Pour in cake batter and smooth with a rubber spatula. Bake until cake pulls away slightly from the sides of the pan, approximately 40 minutes. Test for doneness by inserting a toothpick into the center of the cake – if it is clean or has very few crumbs, the cake is done.
OR if baking cupcakes, line pans with 22-24 cupcake lines or oil well. Fill 2/3 full with batter and smooth tops. Bake for approximately 25 minutes, testing with toothpick for doneness.
Let the cake cool on a wire rack for 10-15 minutes. Run a knife around the edge of the pan, if necessary to release the cake, and invert onto a wire rack if desired.
While cake is baking, bring 1/2 cup sugar and 1/2 cup water to a boil in a small saucepan. Add lemon slices and reduce to simmer for 25 minutes. Remove the lemon slices and set aside; stir 1/4 cup fresh lemon juice into the syrup.
Using a toothpick, poke holes into the warm cake while it is cooling. Pour lemon syrup over top and into the holes. Let cool completely before frosting. Add the cooked lemon slices to the top of the cake for decoration after frosting.