Adjust oven rack to middle position; heat oven to 350 degrees. Spread nuts on large rimmed baking sheet and bake until deep golden brown, 10 to 15 minutes. Transfer nuts to cutting board to cool; chop coarsely and set aside.
While nuts toast, cut 18-inch length foil and fold lengthwise to 8-inch width. Fit foil into length of 13 by 9-inch baking pan, pushing it into corners and up sides of pan; allow excess to overhang pan edges. Cut 14-inch length foil and fit into width of baking pan in same manner, perpendicular to first sheet (if using extra-wide foil, fold second sheet lengthwise to 12-inch width). Spray foil-lined pan with nonstick cooking spray. Whisk flour, baking powder, and salt together in medium bowl; set aside.
Whisk melted butter and brown sugar together in medium bowl until combined. Add eggs and vanilla and mix well. Using rubber spatula, fold dry ingredients into egg mixture until just combined; do not overmix. Fold in chocolate, figs and nuts and turn batter into prepared pan, smoothing top with rubber spatula.
Bake until top is shiny, cracked, and light golden brown, 22 to 25 minutes; do not overbake. Cool on wire rack to room temperature. Remove bars from pan by lifting foil overhang and transfer to cutting board. Cut into 2-inch squares and serve.