Butter the sides and bottom of a 9 by 13 inch (23 by 33cm) pan.
Melt the chocolate in a double boiler or microwave and allow to cool slightly.
Combine the butter and 1 1/4 cups (296ml) of the sugar in the bowl of an electric mixer. Using the paddle attachment, cream on medium speed until light and fluffy. Continuing to mix, add 3 of the eggs and beat well. Stir in the melted chocolate and mix until smooth. Decrease to low speed and stir in the flour and salt.
Spread the chocolate batter in the pan, reserving about 1 cup (236ml) for later use.
Combine the cream cheese and the remaining 3/4 cup (177ml) sugar in a clean bowl of an electric mixer. Using the paddle attachment, beat on medium speed until smooth. Add remaining 2 eggs and the vanilla extract and again beat until smooth.
Spread the cream cheese mixture in an even layer over the chocolate batter. Scatter spoonfuls of the reserved chocolate batter over the cream cheese mixture. With a knife, swirl the chocolate batter into the cream cheese mixture, creating a marble pattern.
Bake the brownies for 50 to 55 minutes until a skewer inserted in the middle comes out with a moist crumb. Cool for at least half an hour before cutting.