
Preheat the oven to 350°F.
In a medium-large saucepan, melt the butter with the 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 it to cool for about 5 minutes.
Stir in the sugar and vanilla 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 a greased 8-by-8-inch or 9-by-13-inch baking pan. (A square pan will result in thicker brownies.) Spread to even out the top and place in the oven.
Bake for 40 minutes, then check the brownies with a toothpick. If they are overly gooey/messy, return them to the oven for 5 to 10 minutes more. (Just be careful not to burn the edges.)
Allow the brownies to cool completely (important!), then sprinkle with powdered sugar and cut into small squares. The brownies are very rich!