Roll piecrust to increase the circumference enough to fit the tart pan. Place piecrust into a removable bottom tart pan and set aside in refrigerator.
Using an electric mixer with a paddle attachment, cream butter and sugar together, whip until light and fluffy, about 2 minutes. Add ground almonds, rum, egg, almond extract and flour; beat until smooth. This is the frangipane. Spread evenly into the chilled tart shell, and refrigerate.
Combine raspberry lager, sugar, lemon juice, zest, cinnamon, cloves, and vanilla bean in a 6-quart stockpot. Bring to a boil for 5 minutes. Add peeled pears, reduce the heat to a simmer, and cook uncovered until pears are tender when pierced, about 20 to 30 minutes. Remove from heat and let cool.
Preheat oven to 375 degrees F.
Remove cooled poached pears from liquid, and halve each lengthwise; removing core and stem. Place each half, cut side down, on a cutting board, and cut crosswise into thin slices. Arrange the fanned pear slices on chilled frangipane evenly. Bake the tart for 40 to 45 minutes or until the shell is golden brown and frangipane is puffed and brown.
In a saucepan, melt the apricot jam and brush the top of the tart with a pastry brush as soon as it comes out of the oven. Cool the tart to room temperature before slicing.
When arranging the pears, try to stretch slices toward the center of the tart, which will elongate the pears a bit and fill the shell better than if the pears were just placed flat.
Make sure to turn pears during cooking process to insure all sides are exposed to poaching liquid.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.