Preheat your oven to 350 degrees. Spray two 9" round pans with non-stick spray. Lay a square of parchment paper in the center of the pan and spray with non-stick spray. This ensures that the cakes will release.
Sift the first four ingredients into a medium size bowl.
In your stand mixer bowl, put the butter and sugar. Use the paddle attachment to beat the mixture on medium until it is pale and fluffy. Once the butter and sugar is mixed thoroughly, add the vanilla and one egg. Turn the mixer back on and beat until the egg is incorporated. Scrape down the sides of the bowl and add another egg. Turn the mixer back on until the egg is incorporated completely and scrape down the sides. Repeat this for the last two eggs.
Now take your milk and dry ingredients and alternately add them to the egg batter. Make sure every time you add the milk or the flour it is completely incorporated before you add more. Otherwise, it may start to look curdled.
I then folded in the peach puree with a spatula into the batter.
I divided the batter into the two 9" cake pans and tapped them on the counter to get the bubbles out. Place them in the oven for about 30 minutes or until they are done.
In the stand mixer, add the butter and beat until pale and creamy.
Add in about 1-2 cups of powdered sugar and beat again until incorporated.
Add in the vanilla and half of the peach puree. Turn the mixer on low and beat until the liquid is mixed in.
Add in another 2 cups of powdered sugar and continue to mix on low speed. Be sure to scrap down the sides and then add the remaining peach puree.
After the puree is beat in, add the remaining powdered sugar. Scrape down the sides and give it another quick mix.