Preheat oven to 350°F. Grease a 9 x 9-inch baking pan.
In a medium bowl, mix together the oil, sugar and vanilla. Beat in the eggs.
In a separate bowl, combine flour, cocoa, baking powder and salt; gradually stir into the egg mixture until well blended.
Spread the batter evenly into the prepared pan. Bake for 20 - 25 minutes, or until the brownies begin to pull away from the edges of the pan.
Let cool completely on a wire rack then place in refrigerator to cool down even more. The brownies are best when they've had time to cool and develop their flavor.
Notes
Source: Adapted from MSPI Mama, originally adapted from AllRecipes.comYou're Gonna Bake It After Allbakeitafterall.com