Cut the cold dough in pieces and reknead into a disc. On a floured table, press the disc, evening the circle as you go, until it is about 6 inches in diameter. Flour the surface of the dough and roll in into a circle measuring about 1 1/2 inches bigger than the 9-inch tart mold. Flour as much as you need to prevent the dough from sticking. Brush off any excess flour, fold the dough in half and center it over the mold. Press along the bottom edge and side to even it. Press any excess dough from the bottom edge up the sides so that they are thicker. Cut off any excess dough with a rolling pin and press the sides up so it extends about 1/8-inch above the rim. Dock the bottom with a fork and freeze.

Preheat oven to 375 degrees. Bake the frozen tart shell until the center barely begins to color, 10 to 12 minutes. Cool completely.

Lower oven to 350 degrees. Combine the nuts and confectioner's sugar in a food processor and process to a fine powder, about 30 seconds. In the bowl of a standing mixer, cream the butter and sugar until fluffy. Add the nut powder and mix thoroughly, scraping down the bowl once or twice. Add the egg in three parts, beating after each addition on medium high speed, until very light and fluffy. Add the almond and vanilla extracts. On low speed, mix in the flour just until incorporated.

Spread the jam on the bottom of the prebaked shell and then spread evenly with the frangipane. Slice the pears in half and core. Cut each half in very thin slices from blossom to stem, leaving them attached at the stem end. Cut off the end pieces and cut each half in quarters. Fan out each quarter and arrange the 6 fans in a circle over the frangipane, stems to the center. Be sure to leave some space between the fans so the filling can rise up around them. Brush the pears lightly with melted butter. Bake about 50 to 55 minutes, until the top is golden brown and crusty. If the rim is getting too dark, cover the edge with foil or pie guards. Cool in the mold on a rack; remove the outer ring after 10 minutes. Slip a flexible metal palate knife between the tart and the metal bottom and slide off the tart. Cool completely on a rack before serving. Cut with a sharp serrated knife.