1 1/2 sticks cold unsalted butter, cut into tablespoons
1 large egg, separated
1/4 cup ice water
6 firm, ripe pears, such as Bartlett or Anjou—peeled, halved, cored and cut
lengthwise into 1/4-inch wedges
2 tablespoons apple jelly, melted
Preheat the oven to 350°. Spread the hazelnuts in a pie plate. Bake for 12 to 14 minutes, or until lightly toasted. Transfer to a kitchen towel and let cool completely, then rub the nuts together vigorously to remove the skins.
In a food processor, pulse half of the hazelnuts until finely chopped. Add 2 cups of the flour, 3 tablespoons of the sugar and the salt and process until the nuts are finely ground. Add all but 2 tablespoons of the butter and pulse until the mixture resembles coarse meal. Whisk the egg yolk into the ice water, add to the processor and pulse until the pastry comes together. Turn the pastry out onto a lightly floured surface and pat it into a 1-inch-thick disk. Wrap in plastic and refrigerate for at least 1 hour.
In a food processor, combine the remaining half of the hazelnuts with the remaining 2 tablespoons of flour and 1/4 cup of sugar and process until finely ground. Add the remaining 2 tablespoons of butter and the egg white and process until the filling is smooth and creamy.
On a work surface, slightly overlap two 18-inch-long sheets of wax paper. Lightly flour the pastry disk and set it in the center of the wax paper. Roll out the pastry to a 16-inch round. Gently flip the pastry onto a parchment-lined baking sheet and peel off the wax paper.
Spread the hazelnut filling over the pastry to within 2 inches of the edge. Arrange the pears over the filling in concentric circles, overlapping them slightly. Fold the edge of the pastry up and over the pears, crimping decoratively. Refrigerate the crostata for 15 minutes.
Preheat the oven to 375°. Bake the crostata in the center of the oven for 1 1/2 hours, or until the pears are tender and the crust is golden. Preheat the broiler. Cover the crostata crust with strips of foil and broil until the pears are browned in spots, 2 to 3 minutes. Slide the crostata with the parchment paper onto a rack to cool. Brush the pears and crust with the melted apple jelly and let cool to room temperature. Cut into wedges and serve.
The pastry can be refrigerated for up to 3 days. The crostata can be baked earlier in the day.