Preheat oven to 325 degrees. Butter sides and bottom of round 9-inch baking dish that's at least 2 inches deep.
Beat eggs and sugar at high speed in mixing bowl until pale yellow ribbons form. Mix in the rum and vanilla. Add flour and mix well. Set aside.
In separate bowl, whip heavy cream until firm peaks form. Carefully fold whipping cream into the egg mixture with a rubber spatula. Pour batter into buttered dish.
Peel and core apple and pear and slice thinly, crosswise into half moons. Arrange over the batter in the dish, alternating the pear and apple slices. The fruit may start to sink into the dough; the fruit will be embedded inside the custard when baking. Place dish in preheated oven and bake approximately 35 minutes or until top is golden brown. Serve warm or chilled.