Place the butter in a medium size saucepan and turn the burner to medium-high heat.
When the butter begins to bubble, stir it constantly for about 3-4 minutes.
As soon as it turns a deep golden brown and you can smell the toastiness of the butter, remove it from the heat and let it cool for about 10 minutes, before transferring it into a dish, covering it and placing it in the fridge to resolidify.
Let it chill in the fridge until it is completely cooled down and solid again. It may take 1-2 hours.
Preheat the oven to 375°F and line a large baking sheet with parchment paper.
Skin and dice the peaches into bite size pieces.
In the bowl of a large food processor, add the flour, granulated sugar, baking powder, and salt and give it a quick pulse.
Cut the solidified brown butter into 1-inch pieces. Turn the food processor on and begin adding the pieces of butter to it, a few pieces at a time until all of it is combined.
Make sure there are no large chunks of butter in it. It should look like sand.
Transfer the flour mixture to a large mixing bowl.
Whisk the egg, milk (or half and half) and vanilla together then add it to the mixing bowl with the dry ingredients.
Mix them together with a fork until it comes together into a crumbly batter.
Gently fold in the peach pieces.
Dump the batter onto the prepared baking sheet and shape the batter together with your hands until it is a smooth circle, about ¾ inches thick.
Carefully cut the scone batter into triangle wedges and separate them on the baking sheet leaving at least 2 inches of space between each one. It should yield 10-12 scones.
Bake them in the oven for 20-25 minutes until they just begin to turn golden on the sides and the tops.
Remove it from the oven and let it cool for 15 minutes until glazing them.
With a spoon, mix the powdered sugar and milk together until it forms a thick glaze or drizzle. You may have to add a little more milk if it is too thick. Drizzle the tops of the scones and let the glaze harden before serving. Enjoy!