Pear and Hazelnut Frangipane Tart
['1 cup hazelnuts, toasted, loose skins rubbed off in a kitchen towel, and cooled', '1/2 cup sugar', '1/4 cup all-purpose flour', '3/4 stick (6 tablespoons) cold unsalted butter, softened', '2 large eggs', '1 teaspoon vanilla extract', '1/2 teaspoon almond extract', '1 tart shell', '3 firm-ripe Bosc or Anjou pears', '1/4 cup apricot preserves', 'heated and strained']
Preheat oven to 350°F.
Pulse hazelnuts with 1/4 cup sugar in a food processor until finely ground, then add flour and pulse to combine.
Beat together butter and remaining 1/4 cup sugar with an electric mixer at moderately high speed until pale and fluffy. Add eggs 1 at a time, beating well after each addition, then beat in extracts. Reduce speed to low and mix in nut mixture until just combined.
Spread frangipane filling evenly in tart shell. Peel, halve, and core pears, then cut lengthwise into 1/4-inch-thick slices, holding slices together to keep pear shape intact. Arrange pears decoratively on filling, fanning slices slightly. Bake until pears are golden and frangipane is puffed and golden brown, 30 to 40 minutes. Brush pears (not filling) with preserves and cool tart completely in pan on rack, then remove side of pan.
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