Instructions

for the filling

 Bring mango, water, and sugar to a boil in medium saucepan over medium heat and cook, stirring occasionally, until mango is softened. Mash mango with potato masher until broken down and continue to cook until mixture has thickened, about 5 minutes. Off heat, stir in lemon juice. Transfer filling to bowl, let cool slightly, then cover and refrigerate until completely chilled, about 1 hour. (Filling can be refrigerated for up to 3 days.)

for the cake

 Adjust oven rack to middle position and heat oven to 350 degrees. Line two 9-inch round cake pans with parchment paper; grease parchment but not pan sides.
 Pulse 1 cup macadamia nuts in food processor until chopped, about 10 pulses. Transfer to bowl and stir in chocolate; set aside for decorating. Add remaining ½ cup macadamia nuts and sugar to now-empty processor and process until finely ground, about 20 seconds. Add flour, baking powder, and salt and pulse to combine, about 5 pulses; transfer to large bowl. Whisk egg yolks, oil, water, and vanilla together in second bowl. Whisk egg yolk mixture into flour mixture until smooth batter forms.
 Using stand mixer fitted with whisk attachment, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip until soft peaks form, 1 to 2 minutes. Gently whisk one-third of whites into batter. Using rubber spatula, gently fold remaining whites into batter until no white streaks remain.
 Divide batter evenly between prepared pans. Gently tap pans on counter to release air bubbles. Bake until tops are light golden brown and cakes spring back when pressed lightly in center, 25 to 28 minutes, switching and rotating pans halfway through baking.
 Let cakes cool in pans on wire rack for 15 minutes. Run thin knife around edges of pans. Remove cakes from pan, discarding parchment, and let cool completely on rack, about 1 hour.

for the frosting

Microwave chocolate in bowl at 50 percent power, stirring occasionally, until melted and smooth, 2 to 4 minutes; let cool. Combine sugar, egg whites, and salt in clean, dry bowl of stand mixer. Set bowl over saucepan filled with 1 inch of barely simmering water, making sure that water does not touch bottom of bowl. Cook, whisking constantly, until mixture registers 150 degrees, about 3 minutes. Remove bowl from heat and transfer to stand mixer fitted with whisk attachment. Whip warm egg mixture on medium speed until it has consistency of shaving cream and has cooled slightly, about 5 minutes. Add butter, 1 piece at a time, and whip until smooth and creamy, about 2 minutes. (Frosting may look curdled after half of butter has been added; it will smooth out with additional butter.)
 Add melted chocolate and mix until combined. Increase speed to medium-high and whip until light and fluffy, about 30 seconds, scraping down sides of bowl as needed. If frosting seems too soft after adding chocolate, chill it briefly in the refrigerator, then rewhip until creamy. (Frosting can be refrigerated for up to 24 hours; warm frosting briefly in microwave until just slightly softened, 5 to 10 seconds, then stir until creamy.)
 Line edges of cake platter with 4 strips of parchment to keep platter clean. Place 1 cake layer on platter. Spread mango filling evenly over top, right to edge of cake. Top with remaining cake layer and spread frosting evenly over top and sides of cake. Press reserved chopped macadamia nuts onto sides of cake. Refrigerate cake until set, about 30 minutes. (Frosted cake can be refrigerated for up to 24 hours; bring to room temperature before serving.)
 Before serving, remove parchment strips. Shingle 3 mango slices on cutting board or counter, overlapping each slice by about ½ inch. Starting at 1 end, roll up slices to form rose shape; place on top of cake. Repeat, arranging mango roses decoratively over top of cake.