Preheat oven to 350 degrees F. Line an 8 inch square metal pan with foil and spray foil with cooking spray (or use nonstick foil).
Make the cream cheese filling first. In a mixing bowl, beat the butter and cream cheese until smooth. Beat in the sugar, then beat in the egg. Stir in the flour and vanilla. Set aside.
Make the brownie batter. In a medium saucepan, melt the butter over medium heat. Reduce heat to low and add the chocolate, stirring over low heat until chocolate is melted. Set aside to cool.
With an electric mixer, beat the eggs for one minute. Gradually add the sugar and beat until thick and pale. Beat in vanilla, baking powder and salt. By hand, stir in the flour. Stir in melted chocolate mixture.
Pour about 3/4 of the batter into the pan. Pour the cream cheese mixture over the chocolate batter. Pour remaining chocolate batter over cream cheese mixture, leaving gaps so the cream cheese shows.
Bake on center rack of oven for 35 to 40 minutes. Let cool to room temperature, then chill brownies until firm. Remove from pan by lifting foil. Place on a cutting board and cut into 16 squares.