Start by preheating your oven to 350°F (175°C). Grease your cake pans well with butter or non-stick spray, and if you’d like an easier release later, line the bottoms with parchment paper. Set the pans aside while you make the batter.
In a large mixing bowl, beat the softened butter together with both the granulated sugar and the brown sugar. Use an electric mixer and keep going until the mixture is light and fluffy—this usually takes about 3 to 5 minutes. This step is key to giving the cake a soft, airy texture.
Next, add in the eggs and the extra egg whites, one at a time. Mix well after each addition, then stir in the vanilla extract. Be sure to scrape down the sides of the bowl so everything blends evenly.
In another bowl, whisk together the cake flour, salt, baking powder, baking soda, and a touch of cardamom (or cinnamon if you prefer). This will be your dry mixture.
Now, bring everything together. Add the dry ingredients to the butter mixture in three parts, alternating with the buttermilk. Start with the dry mixture, then buttermilk, and finish with the dry. Mix on low speed just until smooth—don’t overmix or the cake will lose its tenderness.
Once the batter is ready, gently fold in the diced peaches with a spatula. Stir only enough to spread the fruit evenly throughout the batter.
Divide the batter between the prepared pans and smooth the tops. Bake in the preheated oven for 40 to 45 minutes, or until a toothpick inserted in the center comes out clean. Let the  cakes cool in the pans for about 10 minutes, then turn them out onto a wire rack to cool completely.
While the cakes are cooling, prepare the topping. In a small bowl, toss thin peach slices with honey (or sugar) and a squeeze of lemon juice. Let them sit for 5 to 10 minutes so the juices develop.
Once the  cake is fully cooled, spoon the peach topping over the top. You can serve it just like that, or add a dollop of whipped cream or even a scoop of  vanilla ice cream for extra indulgence.