Put the butter and chocolate into a microwave-safe bowl and heat on high for 1 to 2 minutes, stirring every 30 seconds to melt the chocolate. Set aside.
In another bowl, whisk together the eggs and sugar.
In a large bowl sift the flour with the baking powder and salt. Add the egg and chocolate mixtures along with the vanilla and stir well to combine.
Spray an 8 by 8 by 2-inch or 8-inch round microwave-safe glass pan with cooking spray. Pour the batter into the pan, spread it out evenly, and scatter the chocolate chips on top. Cook on high for 5 minutes. Remove from the oven and let rest for 3 minutes before cutting and eating.