Preparation

Make the puff pastry:

• In a large bowl, combine the flour and salt. Add the butter and toss to coat with flour. Using a pastry blender or two blunt table knives, cut the butter into the flour until the mixture is dry and rough with 1/2- to 3/4-inch chunks of butter. Add 1/2 cup very cold water and continue cutting until you get a shaggy dough that barely hangs together. Turn the dough out onto a lightly floured work surface and pat into a rectangle, then roll into a 6×18-inch rectangle, flouring the rolling pin as necessary. It’s okay if the dough is ragged at first.

  With a pastry scraper, fold both short ends toward each other so they meet in the middle. Fold one half over the other half to make a 4×6-inch rectangle. Turn the dough so that the fold is on the right. Roll into a 6 x 18-inch rectangle and repeat the folding technique. Wrap in plastic; chill for 20 minutes.

  Position the dough so the fold is on the right. Roll into a 6 x 18-inch rectangle and fold the dough again as directed above, flouring lightly if needed. It should be smooth with visible flecks of butter. Divide the puff pastry crosswise into 2 rectangles, one about 3/4 inch longer than the other. Wrap in plastic and refrigerate until well chilled, about 2 hours or overnight.

Make the tart:

• Position a rack in the center of the oven and heat the oven to 425° F

  On a floured surface, roll out the smaller pastry rectangle to a rectangle roughly 9 x 14 inches. Transfer to a parchment-lined baking sheet and trim the edges to get a neat rectangle 8 x 13 inches. Roll out the larger pastry rectangle to roughly 11-1/2 x 14 inches and trim the edges to get a neat rectangle 11 x 13 inches. Cut this rectangle into four 13×3/4-inch strips and four 8 x 3/4-inch strips. (You’ll have leftover dough, which can be refrigerated or frozen for another use).
  Moisten two of the shorter strips with a bit of water and lay them, moistened side down, along the short sides of the smaller rectangle. Moisten two of the longer strips and lay them along the longer sides of the rectangle, overlapping the shorter strips at the corners. Repeat with the remaining four strips, stacking them on the first set of strips to make a double-high edge.

  In a food processor, pulse the hazelnuts until coarsely chopped. Add the sugar and pulse until finely chopped. Add the egg, butter, and vanilla, and process until creamy.

  Spread the hazelnut filling evenly over the bottom of the tart crust, up to the edges. Arrange the sliced pears in a shingled crosswise pattern over the filling, alternating directions with each row. Combine the cinnamon and sugar in a small bowl and sprinkle it over the fruit.

  Bake until the crust is puffed and golden brown and the fruit is tender, about 23 to 26 minutes.