Blend together flour, sugar, baking powder, salt, and butter with your fingertips or a pastry blender (or pulse in a food processor) until most of mixture resembles coarse meal with small (roughly pea-size) butter lumps. Add egg and stir with a fork (or pulse) until a crumbly dough forms.

Turn out dough onto a work surface and divide into 4 portions. With heel of your hand, smear each portion once or twice in a forward motion to help distribute fat. Gather dough together with scraper.

Preheat oven to 375°F.

Press dough evenly onto bottom (but not up sides) of baking pan and bake in middle of oven until edges are golden and begin to pull away from sides of pan, 15 to 20 minutes. Cool in pan on rack.

Make topping:
Bring honey, brown sugar, and salt to a boil in a 2-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 completely coated.

Pour nut mixture over pastry crust, spreading evenly, and bake in middle of oven until topping is caramelized and bubbling, 12 to 15 minutes. Cool completely in pan on a rack. Lift dessert out of pan using foil overhang and cut into 25 squares.

(Honey nut squares keep, layered between sheets of wax paper, in an airtight container at room temperature 1 week.)