Preheat oven to 325 degrees. Lightly grease or butter and flour a 9-by-5-inch loaf pan, and set aside.
Dice 1 peach into small pieces. Pat the pieces dry with a paper towel and set aside.
Add the remaining 2 peaches and the lemon juice to a food processor or blender, and blend on high until completely puréed.
Measure out 1 level cup of the peach purée and transfer it to a mixing bowl with the cooled melted butter, eggs, egg yolk, and vanilla. Whisk to combine and set aside.
Scrape down the sides of the food processor and make the icing using the puréed peaches still remaining in the food processor. Add 1 cup of the confectioners’ sugar to the remaining peach purée in the food processor and blend on high until combined. The icing should be thick but still thin enough to drizzle. Add more confectioners’ sugar to thicken or a splash of water to thin, as needed. Cover and set aside.
In a large mixing bowl, add the flour, granulated sugar, baking powder, and salt, and whisk to combine. Pour the peach mixture from Step 4 into the flour mixture, and whisk well until the batter is thoroughly combined, then fold in the diced peaches.
Transfer the batter to the loaf pan, spread evenly to the edges, and bake until crusty and golden brown on the top and a toothpick inserted into the center comes out clean, 75 to 80 minutes. Remove from the oven and allow to cool for 10 minutes before transferring to a wire rack to cool completely.
Stir the icing and then spread it on top of the warm cake, allowing the extra icing to drip down the sides. Cool the cake to room temperature. Slice and serve or wrap tightly with plastic wrap and store on the counter for up to 3 days.