Melt the butter and chopped chocolate in the saucepan over low heat, stirring for 3 to 4 minutes. Pull the pan off the heat while one or two small pieces still show, and stir until the mixture looks smooth and glossy with no streaks.

Whisk the sugar and vanilla into the warm mixture for 30 seconds. Rest the pan for 5 minutes, until its side feels warm but not hot.

Whisk in the eggs one at a time, beating hard for 40 seconds after each, about 2 minutes in total. The batter is ready when it looks thick and glossy and a ribbon holds on the surface for a few seconds.

Add the flour, cocoa powder, and salt. Fold with the spatula for about 15 strokes, until no dry streaks remain and the batter looks like thick, shiny fudge.

Add the chocolate chips and fold 3 or 4 strokes, until they are evenly scattered.

Scrape the batter into the pan, spread it into the corners, and tap the pan on the counter twice, until the surface looks level and shiny.

Bake on the center rack at 350°F for 30 to 35 minutes, checking at 30. The brownies are done when the edges look set and a toothpick pushed 2 inches from the edge shows a few moist crumbs. Wet batter means 3 more minutes, and a clean toothpick means the pan went too long.

Cool the pan on a wire rack for 1 hour, until the bottom of the pan feels barely warm. Lift the slab out by the parchment and cut 16 squares with a sharp knife, wiping the blade between cuts.