Preheat the oven to 350°F (175°C) and lightly grease a 9x9-inch baking dish.
In a bowl, whisk together the vegetable oil, sugar, and vanilla extract until smooth.
Add the eggs one at a time, mixing thoroughly after each addition.
In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt.
Gradually incorporate the dry ingredients into the wet mixture, mixing gently to avoid overworking the batter.
Pour the batter into the prepared baking dish and spread it evenly.
Bake for 15-20 minutes, or until the edges start pulling away from the pan and a toothpick inserted into the center comes out with moist crumbs.
Let the brownies cool completely on a wire rack, then cut them into squares.