Preheat your oven to 350°F. Line an 8x8-inch square baking pan with parchment paper, leaving a 2-inch overhang on each end and butter the exposed sides.
In a large bowl over a pot with ½-inch of simmering water, stir together chocolate and butter until completely melted, smooth and glossy.
Combine eggs with sugar in a heatproof mixing bowl and set over a saucepan with about ½ inch of simmering water. Whisk constantly until the sugar is completely dissolved in the eggs. It will start to look syrupy and you should feel no grit or granules when you rub it between your fingers.
Use an electric hand mixer to beat eggs with sugar for 2-3 minutes on high speed or transfer to a stand mixer fitted with the whisk attachment and beat until pale, thick and fluffy. When you lift up the beaters, the egg mixture will form a slowly disappearing ribbon on the surface of the mixture when it falls back into the bowl.
Beat in vanilla and salt then stir in warm chocolate mixture until evenly blended. Stir in flour and fold it in until well incorporated and smooth. Fold in chocolate chips.
Pour batter into prepared pan and use the back of the spatula to smooth out the surface. Sprinkle chocolate chips on top. Bake until slightly puffed and a toothpick inserted someplace between the edge and the center comes out with a few moist crumbs, 17-20 minutes. Transfer pan to a wire rack and let cool completely.