Preheat oven to 325 degrees F. Butter the sides and bottom of a 9-inch baking dish that is at least 2 inches deep or a 9-inch springform pan.
Put the whole eggs plus the egg yolks and the sugar in the bowl of a mixer. Beat at high speed until you see pale yellow ribbons form.
Mix in the rum and vanilla. Add the flour and mix well. Transfer to a mixing bowl.
In the clean mixer bowl, whip the heavy cream to firm peaks, then fold it carefully into the egg mixture with a rubber spatula. Pour the batter into the buttered dish.
Peel and core the apple and pear and slice them crosswise into thin half-moons. Arrange over the batter in the baking dish, alternating the apple and pear slices. Do not be concerned if they sink into the mixture; they eventually will end up embedded in it. Place in the pre-heated oven and bake until the top has turned golden brown, 45 to 50 minutes. Serve warm or chilled.
Recipe courtesy of Every Night Italian, Published by Scribner, 2000