Step 3: Prep the Fruit for Your Filling
Start with the mangoes. I don't like to peel the mangoes first, since the thick skin on top of soft fruit leads to a lot of mashed fruit and a very slippery thing that you need to carve a big pit out of. Instead, I segment the mango first and cut the peel off the segments.
Hold the stem end of the mango up. Looking down at the stem, the pit of the mango runs though the widest part. Start by cutting the two "cheeks" of the mango off on either side of the pit, then the smaller pieces that remain. Cut the two large pieces in half, then cut each half in half again. Then, cut the peel off each slice by inserting the blade on one end, and run the knife along the peel while pressing the knife down a bit to hold the peel down as you go, as shown in the fourth photo. Cut the mango into one inch chunks and set aside.
The peaches I peel first, since the skin it too thin to work with like the mangoes. A sharp vegetable peeler works reasonably well. After peeling, run the knife along the "seam" of the peach, all the way around the peach. Grab on either side of the cut (seventh photo), and twist in opposite directions to separate the fruit from the pit (eighth photo). Cut your peaches into slices.
In a mixing bowl, combine the fruit, lime juice, salt, and brown sugar and toss to combine. Transfer the fruit mixture to a colander, and put the colander over the mixing bowl to catch the juice that will run off. Let it sit for 20-30 minutes.