Preheat oven to 350 degrees. Put oil, 1 cup sugar, eggs, salt, and vanilla in the bowl of electric mixer fitted with the paddle attachment, and mix on medium-low speed until combined.
Sift together flour, baking powder, and baking soda into a bowl. Reduce mixer speed to low. Add flour mixture; mix until combined. Stir in pecans.
Divide dough into three equal parts; shape each into a long log about 3 inches wide and 1 inch high. Space logs 4 inches apart on a baking sheet lined with parchment paper. Bake logs until golden, puffed, and just firm to the touch, about 35 minutes. Let cool slightly, 3 to 5 minutes.
Transfer logs to a cutting board. With a serrated knife, gently cut logs into 1/2-inch thick slices. The cookies should still be slightly doughy inside. Work quickly, as slices will crumble if allowed to cool. Transfer slices to baking sheets lined with parchment paper.
Mix remaining 1/4 cup sugar and the cinnamon in a small bowl. Sprinkle cookies with cinnamon-sugar mixture. Bake slices until golden brown and dry, about 15 minutes.