Lightly spoon flour into dry measuring cups, and level with a knife. Combine the flour, sugar, baking powder, and salt. Combine banana, oil, vanilla, and egg in a medium bowl; stir in flour mixture and pecans (dough will be sticky).
Turn dough out onto a lightly floured surface; shape dough into 2 (8-inch-long) rolls with floured hands. Place rolls on a baking sheet coated with cooking spray; flatten to 1/2-inch thickness.
Bake at 350° for 23 minutes. Remove rolls from baking sheet; cool 10 minutes on a wire rack. Cut each roll diagonally into 12 (1/2-inch) slices. Place slices, cut sides down, on baking sheet. Reduce oven temperature to 250°; bake 15 minutes. Turn cookies over; bake an additional 15 minutes (cookies will be slightly soft in center but will harden as they cool). Remove from baking sheet; cool completely on wire racks.