Preheat oven to 425 F. To make the frangipane filling, cream the butter and sugar in the bowl of an electric mixer until light and fluffy.
Add the egg, ground almonds, rum, almond extract, and flour, and beat until smooth. Spread the thick mixture evenly in the chilled tart shell and refrigerate it while you prepare the pears.
Remove the cooled pears from the poaching liquid and cut each in half lengthwise; remove core and stem. Place each half, cut side down, on a cutting board and cut crosswise into thin slices.
Arrange the sliced pear halves on the frangipane around the edge of the tart, leaving space between each half, and place one half in the center of the tart.
When arranging the pears, try to fan the slices toward the center of the tart, which will elongate the pears somewhat.
Bake for 45 minutes, or until the tart shell is golden brown and the frangipane has puffed and browned.
While the tart is baking, bring the reserved poaching liquid to a boil and reduce by half. Brush this glaze lightly over the pears immediately upon removing the tart from the oven. Serve at room temperature.