Combine the chocolate and butter in a medium heatproof bowl and set the bowl over a pot of a simmering water. The bowl should not be touching the bottom on a pot. Stir from time to time until the mixture is melted. Remove from the heat, add sugar, flour and baking powder and mix the ingredients.
Pour ¾ of the brownie batter into the square 9-Inch baking pan covered with parchment paper.
In a separete medium bowl, whisk the mascarpone with the egg, vanilla extract and the remaining ¼ cup of sugar. Evenly spread the mascarpone mixture on top of the brownie batter and cover with the remaining batter. Carefully swirl the mixture a few times using a fork.