For the cookie crust:

1. Put oven rack in middle position and preheat oven to 375°F. Line a 3- by 9-inch baking pan (2 inches deep) with 4 crisscrossed sheets of foil in 2 layers, being careful to press the foil all the way into the corners of the pan and leaving a 2-inch overhang on all sides. Butter foil.
2. Whisk together flour, sugar, baking powder and salt, then blend in butter with a pastry blender or fork, or better yet, pulse in a food processor until mixture resembles coarse meal with pea-size butter lumps. Add egg and stir with a fork (or pulse) until a ball begins to form. You may need to add a tablespoon or so of water if the dough refuses to come together.
3. Turn out dough onto a work surface and lightly knead 5 or 6 times.
4. Press dough evenly onto bottom (but not up sides) of baking pan. If the dough is sticky, dampening your hands will make the dough easier to work with. Bake until edges are golden and begin to pull away from sides of pan, 15 to 20 minutes. Cool in pan on a rack, about 40 minutes.

For the nut topping:

1. Reduce oven temperature to 350°F. Toast hazelnuts on a shallow baking pan until fragrant and golden on the inside, 10 to 12 minutes. Rub hazelnuts in a kitchen towel to remove any loose skins (some skins may remain).
2. Increase oven temperature to 375°F.
3. Bring honey, brown sugar and salt to a boil in a 3- to 4-quart heavy saucepan over moderate heat, stirring until sugar is dissolved, then boil, without stirring, 2 minutes. Add butter and cream and boil, stirring, 1 minute. Remove from heat and stir in all nuts until coated.

4. Spread mixture evenly over crust and bake until topping is caramelized and bubbling, 15 to 20 minutes. Gently press down on the topping with the back of a spatula to slightly compress the topping. Cool completely in pan on a rack. Lift the entire sheet of bars out of the pan using foil overhang and cut into 64 bars. Peel bars from foil.