Preheat oven to 350 degrees F (175 degrees C). Grease a 9x9 inch baking pan.
In a medium bowl, mix together the oil, sugar, and vanilla. Beat in eggs. Combine flour, cocoa, baking powder, and salt; gradually stir into the egg mixture until well blended. Stir in walnuts, if desired. Spread the batter evenly into the prepared pan.
Bake for 20 to 25 minutes, or until the brownie begins to pull away from edges of pan. Let cool on a wire rack before cutting into squares.