Bloom a portion of your gelatin by adding 2 tsp gelatin to a bowl of 1/4 cup water. No need to stir. Just set aside and wait for it to become a gel consistency.
Meanwhile, remove skins and pits from the peaches and mango. Put fruit in a blender or food processor and blend together until fully combined and smooth. It should yield about 1 1/4 cup of puree (about 400 grams).(When fruit is not in season, feel free to substitute with unsweetened fruit puree, found at many specialty food stores.) In a medium pot over the stove, combine the fruit puree, eggs, sugar, and lime juice together on medium heat. Mix together continuously (so the eggs don't scramble) for about 5-8 minutes until it thickens.
Remove from stove and add the butter and prepared bloomed gelatin. Whisk together until combined and smooth. Pour through a strainer into a large bowl. Set aside to cool completely. You can also place in refrigerator to speed up the cooling.
Using a hand or stand mixer, beat 1 cup heavy whipping cream with 1/4 cup powdered sugar. Beat on medium until stiff peaks form.
Add about 1/3 of the whipped cream to the cooled fruit custard and mix together until smooth. This will lighten the custard, making it easier to combine with the rest of the whipped cream. It's okay if you stir this vigorously. Then add the rest of the cream and gently fold together until completely combined.
Pour filling into your baked crust. Place in refrigerator and let it sit for at least 4 hours, or overnight. Top with additional fruit and fresh whipped cream as desired just before serving.
Whipped Cream: To add fresh whipped cream, combine heavy cream and powdered sugar together. Using and hand or stand mixer, beat until stiff peaks form. Pipe or place dollops on slices.