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In a medium bowl, whisk together the eggs, cake and all-purpose flours, salt and 1/4 cup of the milk until smooth. Whisk in the remaining 3/4 cup of milk, the rum and 1 1/2 tablespoons of the sugar. Cover with plastic wrap and let stand at room temperature for 3 hours. Preheat the oven to 450° and coat a deep 9-inch cake pan with half of the butter. Pour the batter into the pan and arrange the pear slices on top. Dot with the remaining butter and bake in the lower third of the oven for 15 minutes. Reduce the oven temperature to 400° and bake for 30 minutes longer, or until the flaugnarde is puffed and deeply golden. Let cool for 2 minutes, then sprinkle with the remaining 1 1/2 tablespoons of sugar and serve.