Preheat the oven to 180°C (350°F) for conventional baking (see note 2 for adjustments if using a convection oven with a fan). Grease an 8x8 inch square cake tin (I use homemade cake release) and then line it with parchment paper, leaving an overhang on two opposite edges. This will help you lift the brownies out of the pan once they're done.
Sift together the flour, cornstarch, and salt. Using a whisk or fork, mix until well combined and set aside.
In a large mixing bowl, add the white sugar and fresh lemon zest. Using your fingers, rub the zest into the sugar until the sugar turns a light yellow color, which should take about 30 seconds.
Next, add the warm melted butter, unflavored vegetable oil, eggs, lemon juice, and vanilla extract. Using a whisk, mix until smooth and combined, but be careful not to overmix, as you don’t want to incorporate too many air bubbles into the batter.
Add the dry ingredients to the wet mixture and, using a spatula, gently fold until just combined. Be sure not to overmix.
Pour the batter into the prepared cake pan. The batter will be thin. Give the tin a little shake to evenly distribute the batter, then drop it lightly on the counter twice. Bake for 22 minutes, or until a toothpick inserted comes out almost clean. You want a small amount of uncooked batter or moist crumbs on the toothpick to ensure the brownies don’t overbake.
Allow the brownies to cool completely in the cake tin for 1-2 hours.
Once cooled, run a thin knife or spatula around the edges of the pan that do not have parchment paper. Carefully use the overhanging parchment paper to lift the brownies out of the pan.
To prepare the lemon glaze, combine the powdered sugar and lemon juice in a small bowl. Stir with a spoon until smooth and combined. The glaze should be thick but spreadable (see note 3).
Spread the glaze evenly over the top of the brownies. Let it set for 30 minutes to an hour until the glaze is firm enough to touch without it sticking to your finger. Once set, slice and serve!