Place the peaches in a food processor and blend until smooth. You should end up with about 3 and 1/2 cups of peach purée. Place the purée in a small saucepan. Cook over medium-low heat, stirring often to prevent burning, until the purée has reduced to 2 cups, about 12-15 minutes. Allow to cool for 10-15 minutes.

Preheat the oven to 350ºF; spray four 6-inch round baking pans with nonstick cooking spray. In a large mixing bowl, stir all of the cake ingredients together until smooth; batter will be thick. Divide the batter evenly among the prepared pans, and bake for 23-25 minutes, or until toothpick inserted in the center comes out with few crumbs attached. Allow to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.

In a stand mixer fitted with the whisk attachment, whip the heavy cream until stiff peaks form; set aside in the refrigerator.

Pour the peach purée into a small saucepan, and stir in the gelatin, sugar, and salt. Cook the mixture over medium heat until it begins to bubble. Remove the mixture from the burner, and stir in the lemon juice and vanilla. Place saucepan over an ice water bath (large bowl filled with ice and cold water), and use a spatula to constantly stir the mixture until it thickens into a pudding-like texture. Fold in the whipped cream until just combined.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and salt together on high until fluffy and pale in color, about 5-6 minutes. Decrease speed to low and slowly add the powdered sugar. Add the vanilla extract, almond extract, and heavy cream and beat until combined. Increase speed to medium-high and beat until light and fluffy, about 4 minutes.

Place one cake layer on a pedestal or plate. Spread a third of the peach mousse evenly over the cake. Place a second cake layer on top, followed by a layer of the mousse. Repeat with the third cake layer and remaining mousse. Place the final cake layer on top and make sure that all sides are straight and lined up. Refrigerate for at least 15 minutes.

Remove cake from refrigerator and frost the entire cake to seal in the crumbs; chill for at least 30 minutes. Meanwhile, tint the frosting. Remove about 3/4 cup of frosting and place in a separate bowl. Tint frosting to desired shade of pink. Remove another 3/4 of untinted frosting and place in a separate bowl. Using yellow and red, tint frosting light orange/peach. I found it easiest to first stir in a good bit of yellow, then adding tiny bits of red to achieve the peach color.

Remove cake from the fridge, and use an offset spatula to spread thick patches of pink and peach buttercream all around the cake. Fill some of the areas with some of the white untinted frosting. Smooth the frosting around the cake as the colors begin to blend together. If there are empty patches, feel free to go over them with more frosting until you get the desired watercolor effect you're looking for.

Sprinkle the top of the cake with pink, orange, and peach sprinkles. Fill a pastry bag fitted with a large round tip with the remaining frosting and pipe some buttercream dollops around the border. I ended up using the frosting that I had scraped off when smoothing the frosting around the cake. Cake will keep covered in the refrigerator for up to 5 days. Allow to sit at room temperature for 15-20 minutes before serving.