Adjust oven rack to middle position and heat oven to 350 degrees. Grease 9 by 5-inch loaf pan; dust with flour, tapping out excess.
Spread nuts on rimmed baking sheet and toast until fragrant, 5 to 10 minutes; set aside.
Stir buttermilk and sugar together in medium bowl. Add melted butter and egg; stir until combined. Stir in dried figs until combined. In another medium bowl, whisk together flour, baking powder, baking soda, salt, and nuts. Stir buttermilk mixture into flour mixture with rubber spatula until just moistened. Scrape batter into prepared pan and smooth surface with rubber spatula.
Bake until loaf is dark brown and skewer inserted in center comes out clean, 55 to 60 minutes, rotating pan halfway through baking. Cool in pan for 10 minutes, then transfer to wire rack and cool at least 1 hour before serving.