Prep the pan. Preheat oven to 350°F. Lightly coat a 9-inch springform pan with nonstick spray, line the bottom with a parchment circle, then lightly spray again.
Make the lime sugar. In a large mixing bowl, combine granulated sugar and lime zest. Rub the zest into the sugar with your fingers until fragrant. Cover and set aside.
Make the crust. Add shortbread cookies to a food processor and pulse into fine crumbs. Drizzle in melted butter and pulse until evenly moistened.
Bake the crust. Press the crumb mixture firmly into the prepared pan, using the bottom of a measuring cup to smooth it evenly. Bake for 10 minutes, then remove from oven and cool. Reduce oven temperature to 325°F.
Mix the cheesecake base. Add cream cheese, flour, and freeze-dried mango powder to the lime sugar. Beat on low speed until combined and smooth.
Add eggs and mango. Add eggs one at a time, mixing on low speed until almost combined after each addition. Scrape down the bowl, add mango puree, and mix on low just until smooth. Do not overmix.
Bake the cheesecake. Pour batter over the cooled crust and smooth the top. Place a large baking pan on the oven rack below the cheesecake and fill it halfway with hot or boiling water. Bake cheesecake at 325°F for 47–55 minutes, until the edges are set and the center still jiggles slightly.
Cool slowly. Turn off oven and leave cheesecake inside with the water pan, door slightly ajar, for 60 minutes.
Make the mango lime curd. While cheesecake bakes, add sugar, eggs, egg yolks, mango puree, lime juice, butter, and lime zest to a heatproof bowl set over a saucepan with simmering water. Whisk constantly until thickened, about 10 minutes.
Chill the curd. Remove curd from heat. Press plastic wrap directly onto the surface and refrigerate until completely chilled. Once chilled, strain through a fine-mesh strainer, then stir in lime zest if desired. Cover and refrigerate until needed.
Cool the cheesecake. Remove cheesecake from oven and carefully run a knife around the top edge to loosen it from the pan. Cool to room temperature, then refrigerate at least 1 hour before adding the mousse.
Whip the first cream mixture. Add 1/2 cup heavy cream and 1/4 cup powdered sugar to a mixing bowl. Whip until stiff peaks form, then transfer to a small bowl and set aside.
Make the mango lime mousse. In the same mixing bowl, add mango lime curd, remaining 1/4 cup powdered sugar, E-Z Gel, and kosher salt. Whisk until combined. Add remaining 1 cup heavy cream and whip until stiff peaks form.
Fold and spread. Fold the reserved whipped cream into the mango lime curd mixture until combined. Spread mousse over the chilled cheesecake, smoothing it to the edges.
Chill until set. Refrigerate cheesecake for at least 2–3 hours, or until the mousse is completely set.
Release and garnish. Run a hot knife around the edge of the mousse, then release the springform pan. Transfer cheesecake to a cake plate and garnish with sliced mangoes, lime slices, and lime zest as desired. Serve chilled.