Preheat oven to 350F. Line 3, 8-inch cake pans with parchment paper; set aside.

Prepare the peach puree. Place peaches (use fresh or canned) along with 1/4 cup sugar into a food processor. Pulse until peaches are pureed. Measure out 3/4 cup peach puree for the cake batter. Set aside the remaining puree to soak the cake layers.

Prepare the cake batter. Cream together the butter and sugar until light and fluffy. Add the eggs, vanilla, and peach extract (optional; may be hard to find in stores). Beat until the mixture is smooth and creamy. Add the milk and 3/4 cup peach puree. In a separate bowl, combine the dry ingredients: flour, baking powder and salt. Add the dry ingredients to the batter and whisk just until combined.

Divide the cake batter between three bowls. Leave one bowl plain, color the second and third bowls with peach food coloring, making one darker than the other. Pour the cake batter into the prepared pans and bake in preheated oven for about 35 minutes, or until a toothpick inserted into the center comes out clean. Remove the cakes from the oven, cool in the pans for 10 minutes, then on wire rack until completely cooled.

Prepare the cream cheese frosting. Place the softened butter and cheese into a stand mixer bowl and whisk on high speed for about 5 minutes, until light and fluffy, scraping sides of bowl often. Add the vanilla extract, salt and peach food coloring, then gradually add the confectioner's sugar. Add the sugar a cup at a time and whisk after each addition.

Assemble the cake. Pierce each cake layer with a fork and soak with the remaining peach puree. Layer the darkest cake layer on the bottom, spread a generous amount of frosting between each layer. Frost the top and sides with a crumb coat layer first, then refrigerate cake for about 20 minutes. The apply a second layer of frosting and smooth the top and sides. Refrigerate the cake again for another 20 minutes.

Meanwhile, prepare the white chocolate ganache. Combine the white chocolate with the heavy cream in a large bowl. Use a water bath or microwave and heat the white chocolate until completely melted. Add a bit of white food coloring; this will make the ganache less transparent. Allow the ganache to thicken slightly, then transfer into a pastry bag or ziplock bag. Drizzle the ganache down the sides of the cake first, then spread with a spatula over the top.

Garnish the cake with gummy peach rings. Keep cake refrigerated. Remove from the refrigerator about 1 hour prior to serving to allow the frosting to soften.