Game plan: We prefer the snappiness that baking on a baking sheet gives to the crust, but if you prefer a softer crust, bake directly on the oven rack.
The dough for the crust can be made up to 2 days ahead. Keep it refrigerated, then proceed from step 4. The filling can be made up to 2 days ahead; keep it chilled. And the tart can be made up to 8 hours ahead; let it stand at room temperature.
5 tablespoons unsalted butter, cut into large pieces
1 1/4 cups all-purpose flour
1 large egg yolk
For the filling:
3/4 cupwalnuts, toasted
1/3 cup granulated sugar
2 tablespoons unsalted butter (1/4 stick), cut into large pieces
1 large egg white
1 large egg
2 tablespoons all-purpose flour
1/4 teaspoon fine salt
For the pears:
1/4 cup granulated sugar
1/4 cuppear brandy
1 tablespoon freshly squeezed lemon juice
3 medium-size firm but ripe Bosc pears
For the crust:
Combine sugar, walnuts, and salt in a food processor fitted with a blade attachment and process until nuts are evenly ground and mixture resembles whole-wheat flour, about 15 seconds. Add butter and process until smooth and mixture just comes together, about 10 seconds.
Add flour and egg yolk and pulse until incorporated, about 15 times. Scrape down the sides of the bowl and continue to pulse until dough is evenly combined and holds together in chunks when squeezed, about 15 to 20 pulses more.
Turn dough out onto a piece of plastic wrap and form into a flat disk. (The dough will be crumbly.) Wrap tightly and refrigerate at least 30 minutes.
Heat the oven to 400°F and arrange a rack in the middle. Crumble the chilled dough into a 9-inch tart pan with a removable bottom. Evenly press it into the sides and bottom using the bottom of a measuring cup dipped in flour.
Line the crust with aluminum foil and fill it with dried beans or pie weights. Bake on a baking sheet until the sides are set, about 15 minutes. Remove the foil and beans and continue to bake until the sides are golden and the bottom is set, about 5 to 10 minutes more. Cool in the pan on a wire rack, about 40 minutes. Reduce the oven temperature to 350°F.
For the filling:
Meanwhile, combine walnuts and sugar in a food processor fitted with a blade attachment. Pulse until walnuts resemble coarse cornmeal and are evenly ground, about 20 pulses.
Add butter, egg white, egg, flour, and salt and pulse until smooth, about 20 pulses. Remove to a small bowl and set aside.
For the pears:
Place sugar, brandy, and lemon juice in a large nonreactive bowl and stir to combine.
Halve, core, and cut pears lengthwise into 1/4-inch-thick slices. Coat in sugar mixture and macerate until pears begin to release some juice, about 15 minutes.
Spread walnut filling evenly in cooled crust.
Place pears in a fine mesh strainer over a bowl to drain, reserving the juices. Arrange the longest and most uniform pieces of pear over the filling (like spokes in a wheel), overlapping, leaving 1/4 inch of edge exposed. (You will have some pieces left over to snack on or discard.)
Bake tart on a baking sheet until golden and a cake tester inserted into the center comes out clean, about 40 to 45 minutes. Place on a rack to cool.
Meanwhile, strain reserved pear juices through a fine mesh strainer into a small saucepan and bring to a boil over medium-high heat. Reduce heat to low and simmer until liquid is reduced by 1/2, about 7 to 10 minutes. (You will have about 3 tablespoons of syrup.) Let cool slightly and then evenly brush syrup over warm tart. (You will have some syrup left over.)
Once tart has cooled, push the pan bottom up to release the tart. Cut into wedges and serve with ice cream, whipped cream, or crème fraîche.