Preheat the oven to 350° and line an 8x8-inch glass pan*** with parchment paper, or grease well with butter.
Melt the butter and baking chocolate together in a microwave safe bowl. Microwave in 15 second intervals, whisking between each interval. When fully melted, whisk in the sugar. Let the mixture cool until almost room temperature. (Take care not to add the eggs too soon, or they'll scramble in the hot mixture.)
Add the eggs and vanilla and beat with a hand mixer on high for 2-3 minutes or until lightened in color and fluffy. (Don't skip this step - beating the eggs well is what gives the brownies that characteristic crackly top.)
Add the cocoa powder, flour, baking powder and salt. Stirring just until incorporated. Last, fold in the chocolate chips or nuts, if desired. Spread the batter into the prepared pan.
Bake at 350° F for 28-32 minutes or until the tops of the brownies are shiny and crackly and the center doesn't wiggle when you shake the pan.
Remove from the oven and let cool for at least 20 minutes. When ready to serve, use the parchment paper to lift the brownies out of the pan before cutting.
Serve warm or cooled completely. The brownies will store tightly covered on the counter for 1-2 days or in the freezer for a couple weeks.