Preheat the oven to 325° F. Then prepare your pan. You can use a loaf pan or a bundt pan. Ensure the pan is large enough since this recipe makes a large-pound cake. Lightly butter and flour on all sides of the pan and set aside.
Melt the butter and set aside to cool.
Prep the peaches. Clean and pit the peaches, leaving the skin on. Take one peach and cut it into 1/2-inch pieces; set aside; you will use this in the batter. Place the other 2-3 peaches and one tablespoon of freshly squeezed lemon juice in a blender or food processor. Blend on high until the peaches are completely puréed. Set aside.
In a large mixing bowl, add the melted butter, eggs, egg yolk, vanilla, and 1 cup of the peach purée. Whisk to combine the wet ingredients.
In a second large bowl, combine the dry ingredients: flour, granulated sugar, baking powder, and salt. Add the peach mixture to the flour mixture, whisking until combined. Fold in the diced peaches. Pour the pound cake batter into the prepared pan.
Transfer to the preheated oven and bake for at least 80 minutes (it can take even longer to bake all the way through). The cake should be golden brown, and a toothpick or knife should come out clean when inserted into the center of it. Remove from the oven and allow to cool for 15 minutes before removing from the pan and cooling on a wire rack.
Make the glaze. Using the remaining peach purée, add 1 cup of confectioners' sugar and blend. It should be a pourable consistency, suitable for drizzling over the cake. If it is too thick, add some water or lemon juice (just a little bit) and blend. If it's too thin, add more sugar and blend.
While the cake is still slightly warm, pour the glaze over it, allowing it to coat the top and drip down the sides. Cool completely before cutting.