Heat oven to 325 (160C) degrees with a rack positioned in the center.
Coat an 8-inch square baking pan with olive oil. Cut a piece of parchment to fit just the bottom of the dish and oil that too.
Sift the flour, cocoa and salt into a bowl (a mesh strainer is perfect for this job).
Beat the eggs in the bowl of a heavy duty mixer fitted with the paddle attachment on medium speed for a minute. Increase speed to medium-high while adding the sugar ½ cup at at time. Beat until the eggs are pale, thick and creamy.
Decrease mixer speed and slowly add the oil in a thin stream, as if you were making an emulsion like mayonnaise. Add the vanilla extract.
Stir the flour mixture into the egg mixture in 3 or 4 additions until just incorporated, scraping down the bowl as needed.
Scrape the batter into the prepared baking dish, using a stiff spatula (the batter is thick and sticky). Sprinkle the cacao nibs over the top, if using.
Bake 30-33 minutes, or until a toothpick inserted into the center of the brownies emerges with some moist crumbs.
Cool the pan completely on a rack before cutting into serving pieces.
Notes
The brownies will keep well 1-3 days at room temperature.
If you don't love the taste of olive oil, substitute with a roasted nut oil such as hazelnut or walnut, or a neutral oil like canola or avocado.
Be sure your using unsweetened cocoa powder, not cacao powder. Cacao is made from unroasted cocoa beans and will add a bitter taste to the brownies.
Note on salt: I bake with Diamond kosher salt, which is about half as salty as other brands of kosher salt. Reduce the amount of salt by half if you're not using Diamond.