Place an oven rack in the center position and preheat the oven to 350°F (175°C). Line an 8x8 pan with parchment paper, leaving overhang on two sides, and chop the pecans into small pieces.
Whisk flour, brown sugar, and salt in a large bowl. Add softened butter and beat on low speed for 1 to 2 minutes until the mixture looks like damp, coarse sand that clumps when squeezed.
Tip the crumbs into the lined pan and press firmly into an even layer using your fingertips and the flat bottom of a measuring cup. Prick all over with a fork about every half inch.
Bake for 18 to 20 minutes until the edges are pale golden and the surface looks dry and lightly browned. Keep the oven on and make the topping while the crust bakes.
Whisk the egg until smooth, then add brown sugar, maple syrup, and vanilla, whisking until glossy with no streaks of egg. Fold in the chopped pecans with a spatula until coated.
Pour the pecan mixture over the hot crust and spread to the edges. Bake for 12 to 15 minutes until the center no longer jiggles and the edges are bubbling and lightly golden.
Run a thin knife around any edges not covered by parchment, then cool in the pan on a wire rack for at least 1 hour until room temperature. Do not cut warm squares.
Lift the slab out using the parchment overhang and cut into a 4 by 4 grid to make 16 squares, wiping the blade clean between cuts. Dust with powdered sugar just before serving, if you like.