Prep. Center a rack in the oven and preheat the oven to 350°F. Sift the flour and salt together; set aside.
1 ¼ C All-Purpose Flour, 1 teaspoon Salt
Melt the butter and chocolate together in a medium saucepan over low heat, stirring frequently and keeping a watchful eye on the pot to make certain the chocolate doesn't scorch (Alternatively, you can melt the ingredients in the top of a double boiler over, not touching, simmering water.)
8 oz Unsalted Butter, 4 oz Unsweetened Baking Chocolate, 2 oz Bittersweet Baking Chocolate
Sweeten. Add 1 cup of the sugar to the mixture and stir for half a minute, then remove the pan from the heat and stir in the vanilla. Pour the mixture into a large bowl.
2 C Sugar, 1 teaspoon Vanilla Extract
Temper Eggs. Put the remaining 1 cup sugar and the eggs into a bowl and mix or whisk by hand just to combine. Little by little, pour half of the sugar and eggs into the melted chocolate mixture, stirring gently but constantly with a rubber spatula so that the eggs don't set from the heat.
1 teaspoon Vanilla Extract, 4 large Eggs
Whip Eggs. Fit the whisk attachment to the mixer and whip the remaining sugar and eggs until they are thick, pale, and doubled in volume, about 3 minutes.
2 C Sugar, 4 large Eggs
Fold. Using the rubber spatula, delicately fold the whipped eggs into the chocolate mixture. When the eggs are almost completely incorporated, gently fold in the dry ingredients with ½ of the chocolate chips.
Assemble. Pour and scrape the batter into an unbuttered 9-inch square pan. Top with remaining chocolate chunks and a sprinkle of flaky sea salt.
Bake. Bake the brownies for 26-32 minutes, during which time they will rise a little and the top will turn dark and dry.
Test the center with a toothpick at about the 28-minute mark to see how the brownies are progressing: they'll be perfect if they're just barely set (with barely any wiggle in the very center) and dry on top, but still pretty gooey. (They're still very good on the other side of set, so don't worry if you slightly overdo it on your first try.)
Cool the brownies in the pan on a rack before slicing into squares. I personally find that refrigerating them for about an hour after they cool to room temp will yield a more set (but still gooey) center. Cool the brownies in the pan on a rack until room temperature. Chill in the fridge for another hour before slicing for clean edges.