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1
Peel and slice the oranges: Using a sharp paring knife, slice off the bottom and the top of each orange, exposing the flesh underneath; following the curve of the fruit, cut a one-half to 1-inch wide vertical strip of the peel; repeat, working your way around the orange until you've cut away all the peel; trim any white pith.
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2
Slice the orange into quarter-inch slices and place in a baking dish (a 12-inch round dish works well).
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3
Repeat, using all of the oranges.
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4
In a small heat-proof bowl, combine the egg yolks, sugar, orange juice, rum, lemon juice and orange zest and stir to combine with a whisk.
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5
Place the bowl over a small pan of simmering water, like a double-boiler, and continue stirring with the whisk; the mixture will foam a little, then turn pale and finally thicken after about 3 to 5 minutes.
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6
When the mixture is thick enough that the whisk leaves tracks in it, remove the bowl from the heat, whisk rapidly to cool it down, and pour it through a fine strainer into a clean bowl.
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7
Cover with plastic wrap and refrigerate (the dish can be prepared to this point up to 8 hours in advance and refrigerated separately).
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8
When almost ready to serve, beat the whipping cream with a balloon whisk until it forms stiff peaks.
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9
Stir the egg mixture to loosen it, adding any orange juice that has collected in the bottom of the baking dish.
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10
Gently fold the egg mixture into the whipping cream.
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11
Sprinkle the oranges with the powdered sugar and stir to combine.
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12
Spoon the egg mixture over the oranges in a haphazard pattern (there won't be enough to completely cover the fruit, so don't worry).
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13
Sprinkle with the slivered almonds and place the baking dish under a cold broiler as close to the flame as possible.
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14
Turn on the broiler and heat just until the gratin puffs and browns, about 4 to 5 minutes.
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15
Alternatively, you can brown the top with a creme brulee torch. Serve immediately.
