Preheat the oven to 350°F (177°C) and grease a 9×13-inch pan or line with aluminum foil or parchment paper, leaving an overhang on the sides to lift the finished brownies out. Set aside.

In a microwave-safe bowl, combine the butter and half (2 ounces) of the chopped chocolate. Melt in 30-second increments, whisking after each, until completely smooth. Whisk in the sugar until completely combined, then whisk in the eggs and vanilla.

Add the cocoa powder, flour, salt, remaining chopped chocolate, and the chocolate chips. Fold it all together with a silicone spatula or wooden spoon. Spread evenly into prepared pan.

Bake for 30 minutes, then test the brownies with a toothpick. If it comes out with wet batter, the brownies are not done. If there are only a few moist crumbs, they are done. Keep checking every 2 minutes.

Remove from the oven and place on a wire rack to cool completely in the pan before cutting into squares.

Cover and store leftover brownies at room temperature for up to 1 week.