Step 1

To make the crust: In a food processor, combine the flour, walnuts, and salt. Process until the walnuts are thoroughly ground into the flour, about 10 seconds. Transfer the mixture to a bowl and chill in the freezer for 30 minutes.

Step 2

Return the flour mixture to the food processor and add the grated butter. Process until butter is incorporated but little flecks remain throughout, about 5 seconds. Add the ice water and pulse briefly, just until the water is distributed evenly and the dough begins to come together into large pieces.

Step 3

Turn the dough out into a 14- x 4.5-inch rectangular tart pan with a removable bottom. Use your fingers press it into the pan evenly, making sure to get it firmly into the corners. Do this quickly to avoid warming the dough.

Step 4

Place a piece of parchment paper on top of the crust, then pour in a single layer of pie weights or uncooked beans. Refrigerate for 20 minutes.

Step 5

While the crust chills, preheat the oven to 375°F.

Step 6

Place the tart pan on a baking sheet lined with parchment paper or aluminum foil. Bake until the butter in the crust has begun to steam and bubble a bit around the edges, about 12 minutes. Remove from the oven, remove pie weights and parchment, and allow the crust to cool to room temperature.

Step 7

To make the poached pears: Peel the pears, then cut them into quarters and remove the cores. In a medium (2-quart) saucepan, heat the water, sugar, spices and vanilla over medium-low heat, stirring until the sugar has dissolved completely.

Step 8

When the sugar has dissolved, add the quartered pears. Bring up to a rapid simmer, then turn down to low and simmer, covered, until the pears are cooked through but still firm, about 10 minutes.

Step 9

Use a slotted spoon to transfer the pears to a wire rack. Let them cool until you can handle them comfortably. Slice each pear quarter into 1/4-inch thick wedges.

Step 10

To make the frangipane: In a food processor, combine all ingredients and process into a thick, smooth batter.

Step 11

To assemble the tart: When ready to bake, preheat the oven to 350°F.

Step 12

Place the crust in its tart pan on a baking sheet lined with parchment or aluminum foil. Pour the frangipane batter into the cooled crust. If you made the frangipane in advance and kept it chilled, it will have thickened slightly — use an offset spatula to spread it into an even layer. Gently layer overlapping slices of pear down the middle of the tart. Don’t worry if the pears sink into the batter a bit — the batter will rise and puff up around them as it bakes.

Step 13

Bake the tart until the frangipane is golden brown and puffy, 45 to 55 minutes. Remove it from the oven and allow it to cool completely.

Step 14

To unmold the tart, push the base of the pan up from the bottom and put aside the frame. Leave the base of the pan underneath the tart and carefully slide it onto a serving plate. Cut into slices and serve with whipped cream or vanilla ice cream and a sprinkle of cinnamon, if desired.