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1
Standing each mango upright, remove flesh from pit by cutting a thick lengthwise slice from each broad side.
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2
(Be careful: Peeled mango is slippery.)
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3
Put slices on a work surface and cut lengthwise into 3/8-inch-thick slices.
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4
Melt butter in a small heavy saucepan over moderate heat, then stir in brown sugar.
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5
Simmer, stirring, until butter is incorporated, 1 to 2 minutes.
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6
Spread mixture in bottom of a buttered 9- by 2-inch round baking pan and arrange mango on top, overlapping slices.
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7
Preheat oven to 350F.
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8
Whisk together flour, baking powder, and salt.
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9
Beat together butter and sugar in a large bowl with an electric mixer at high speed until light and fluffy, about 6 minutes.
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10
Add whole egg and yolks 1 at a time, beating well after each addition.
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11
Beat in vanilla.
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12
Add half of flour mixture and mix at low speed until just combined.
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13
Mix in mango nectar, then add remaining flour mixture, mixing until just combined.
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14
Beat egg whites in another bowl with cleaned beaters until they just hold stiff peaks, then fold into batter gently but thoroughly.
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15
Gently spoon batter over mango topping and spread evenly.
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16
Bake in middle of oven until golden brown and a tester comes out clean, 55 to 60 minutes.
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17
Cool cake in pan on a rack 10 minutes.
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18
Run a thin knife around inside edge of pan, then invert a plate over pan and invert cake onto plate.
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19
Cool completely on plate on rack.
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20
Serve cake at room temperature.
