Lightly spoon flours into measuring cups; level with a knife. Combine flours and next 4 ingredients (through salt) in a large bowl; stir with a whisk. Make a well in center of mixture.
Place buttermilk, figs, oil, vanilla, and egg in a food processor; process until well blended. Add fig mixture to flour mixture, stirring just until combined. Divide batter evenly among 12 muffin cups coated with cooking spray.
Combine brown sugar, oats, and butter in a small bowl; toss with a fork until combined. Sprinkle oat mixture evenly over muffins. Bake at 400° for 18 minutes or until a wooden pick inserted in center of a muffin comes out clean. Cool in pans on a wire rack for 5 minutes; remove muffins from pans, and cool completely on rack.