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.
Slice the orange into quarter-inch slices and place in a baking dish (a 12-inch round dish works well).
Repeat, using all of the oranges.
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.
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.
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.
Cover with plastic wrap and refrigerate (the dish can be prepared to this point up to 8 hours in advance and refrigerated separately).
When almost ready to serve, beat the whipping cream with a balloon whisk until it forms stiff peaks.
Stir the egg mixture to loosen it, adding any orange juice that has collected in the bottom of the baking dish.
Gently fold the egg mixture into the whipping cream.
Sprinkle the oranges with the powdered sugar and stir to combine.
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).
Sprinkle with the slivered almonds and place the baking dish under a cold broiler as close to the flame as possible.
Turn on the broiler and heat just until the gratin puffs and browns, about 4 to 5 minutes.
Alternatively, you can brown the top with a creme brulee torch. Serve immediately.