Preheat the oven to 350 degrees F. Grease an 18-by-13-inch rimmed baking sheet (half sheet pan) with cooking spray.
In a medium-large saucepan, heat the butter and unsweetened chocolate over low heat, whisking occasionally, until smooth and melted. Sprinkle in the cocoa powder and whisk to combine. Remove the pan from the heat and allow to cool for about 5 minutes.
Stir the sugar and vanilla into the chocolate mixture until just combined. One at a time, stir in the eggs. Gently stir in the flour until halfway incorporated. Add the chocolate chips and stir just until combined.
Pour the batter (it will be very thick!) into the prepared pan, spreading to even out the top. Bake for 30 minutes, then check the brownies with a toothpick. If they are overly gooey/messy, return to the oven for 5 to 10 more minutes (just be careful not to burn the edges; see Cook's Note). Allow to cool completely (important!), then cut into small squares.
When warm, the brownies will seem overly gooey/soft. As they cool, they will firm up. (Brownies are best several hours after baking, or even the next day!)