Preheat the oven to 350 degrees F and butter a 9-inch square pan. Lining it with parchment paper is helpful as well. In a double boiler or a heatproof bowl set over a small saucepan of simmering water, melt the butter and bittersweet chocolate together, stirring often to avoid scorching. Set it aside off the heat.
In a big bowl, whisk both sugars, the eggs and yolks. Whisk in the salt and vanilla. Add the melted butter and chocolate and whisk to just combine.
Gradually stir in the flour and mix until everything is combined and smooth. Stir in the chocolate chips.
Scrape the batter into the prepared pan and bake for 35 to 45 minutes, or until a toothpick inserted into the middle displays as much goo on it as you want to see in the middle of those brownies!
Let the brownies cool in the pan on a rack for about 45 minutes. Brownies need time to set, and if you try to cut them while they are too warm, they will fall apart and ruin your day. Slice them at room temperature or colder, and if you want them warm, just put them in a hot oven for a minute or two. Serve the brownies with ice cream, duh!