Preheat the oven to 325° F. Line the baking sheet with a silicone mat or parchment paper. Set aside.
In a small bowl, mix 2 tablespoon cornstarch with 4 tablespoon of water and set aside.
Sift together the flour, baking powder, and salt in a medium bowl. Set aside.
In a stand mixer fitted with a paddle attachment, cream the butter and sugar on medium to high speed until light and fluffy. Scrape down the sides of the bowl.
Add the cornstarch and water mixture, vanilla, and beat until everything is well combined. Scrape down the sides of the bowl again.
Turn the mixer on low, add the dry ingredients, and mix to combine. Next, add the chopped pistachios, pineapples, and mangos and mix to distribute thoroughly. However, make sure not to overmix.
Place the dough onto a prepared baking sheet and divide it into two equal parts. Shape each dough into a log about 9 inches long and 2 inches wide.
Keep both the logs on a baking sheet with at least 3 inches of space between them. If using a small baking sheet, bake one log at a time.
Bake in preheated oven for 25 to 30 minutes or until the top is firm to touch and a toothpick inserted into the center comes out clean.
Remove from the oven and allow to cool on the cookie sheet. When the logs are still slightly warm, carefully transfer them to a cutting board.
Use the serrated knife to cut the logs into even diagonal slices. There will be a total of 22-26 pieces.
Transfer the biscotti back onto a baking sheet, laying them flat and just a small space between them.
Return the biscotti to the oven and bake them again at 325° F for 15 minutes or until they just begin to brown around the edges.
Remove from the oven and allow the biscotti to cool on the baking tray.
The biscotti can be kept in an airtight container for at least two weeks.