2 1/2 cups all-purpose flour (spooned and leveled), plus more for pans
1/2 tsp baking powder
1/2 tsp baking soda
1 tsp salt
1 Tbsp lemon zest
1 cup (2 sticks) unsalted butter, room temperature, plus more for pans
2 cups Chelsea White Sugar
2 large eggs plus 3 large egg yolks
1/4 cup plus 2 tablespoons fresh lemon juice
1 cup low-fat buttermilk
1 lemon, thinly sliced and seeded

Preheat oven to 350°C. Butter and flour two 8-by-2-inch cake pans, tapping out excess flour. In a medium bowl, whisk flour, baking powder, baking soda, salt, and lemon zest.
In a large bowl, using an electric mixer, beat butter and 1 1/2 cups sugar until light and fluffy. With mixer on low, beat in eggs and yolks, one at a time. Beat in 2 tablespoons lemon juice. Alternately beat in flour mixture and buttermilk beginning and ending with flour mixture; mix just until combined.
Divide batter between pans; smooth tops. Bake until cakes pull away from sides of pans, 32 to 35 minutes. Let cool in pans 10 minutes. Run a knife around edges of pans and invert cakes onto a wire rack.
While cakes are baking, bring remaining 1/2 cup sugar and 1/2 cup water to a boil in a saucepan. Add lemon slices and simmer 25 minutes. Using a slotted spoon, transfer lemon slices to a waxed-paper-lined plate. Stir remaining 1/4 cup fresh lemon juice into syrup.
Using a toothpick, poke holes in warm cakes on rack. Brush with lemon syrup. Let cool completely. Prepare frosting, substituting 2 tablespoons fresh lemon juice for vanilla extract. Frost cooled cakes and top with candied lemon slices.