Preheat oven to 425 degrees. Roll out dough into a 12-inch round on a lightly floured surface. Fit into a 10-inch tart pan with a removable bottom and fold over to make a double-thick edge. Roll rolling pin over edge of tart pan to trim dough, and pierce bottom of dough all over with a fork. Freeze until firm, about 15 minutes.
Cream butter and sugar in the bowl of an electric mixer until light and fluffy. Add egg, ground almonds, rum, almond extract, and flour; beat until smooth. Spread the thick mixture evenly in chilled tart shell and refrigerate while preparing pears.
Remove cooled poached pears from poaching liquid and cut in half lengthwise, removing the core and stem. Reserve poaching liquid. Place each half, cut side down, on a cutting board, and cut crosswise into thin slices. Arrange sliced pear halves on frangipane filling around edge of tart, leaving space between each half, and place one half in center of tart. When arranging pears, try to "pull" slices toward center of tart, which will elongate pears a bit and fill the shell better than if the pears were just placed flat. Bake for 10 minutes, reduce oven temperature to 400 degrees, and bake until tart shell is golden brown and frangipane has puffed and browned, 25 to 35 minutes more.
While tart is baking, bring reserved poaching liquid to a boil and reduce by half. Brush this glaze lightly over pears immediately after removing tart from oven. Serve at room temperature.