Preheat oven to 400F degrees. Line bottom of an 8-by-3-inch round cake pan with parchment paper and butter only the bottom of the pan (so the cheesecake can rise). If using a springform pan; wrap the bottom and sides with foil, so the seams are covered.
Separate eggs. Place whites in the bowl of an electric mixer fitted with the whisk attachment; place yolks in a small bowl.
Place softened cream cheese, oil and mango puree and egg yolks in a separate bowl and mix until well combined and smooth.
Beat the egg whites on medium speed until you start to see the wires of the whisk leave a trail in the whites. Slowly add superfine sugar, a tablespoon at a time while beating. Continue to beat until whites are fluffy and hold a soft peak when beaters are lifted.
Gently fold about one-quarter of the whites into the mango mixture to lighten it. Then gently fold in remaining whites, taking care not to deflate batter. Pour into prepared pan.
Place cake pan in a roasting pan, fill the larger pan with enough hot tap water to come one-inch high of the way up the sides of the cake pan.
Bake until top of the cake is golden and doesn’t give when you press it gently in the middle, 35 to 40 minutes.
Turn off oven and crack the oven door so that it cools off. Leave cheesecake in the cooling-off oven for 2 hours so it cools slowly, which keeps the top from cracking.
Lift cheesecake pan out of water and place on a wire rack. Let cool for another 2 hours. Cheesecake will deflate slightly.
Run a knife around the edges of the cheesecake to loosen it from sides of pan. Remove sides of springform pan. If you used a regular cake pan, invert the cake onto a plate, lift off pan, peel off parchment, then invert it right side up on a serving plate.
Chill cake for at least 2 hours before serving. Cake can be stored, well wrapped, for up to 4 days in the refrigerator. Sift confectioners’ sugar over top of cake just before serving.