Preheat the oven to 350°F. and butter and flour a 13- by 9-inch baking pan.
In a metal bowl set over a pan of barely simmering water melt chocolate with butter, stirring, and cool. Whisk in sugar and eggs, 1 at a time, and whisk in (either by hand or with an egg beater) the vanilla and salt. Stir in flour until just combined.
In a bowl with an electric mixer cream together cream cheese and sugar until light and fluffy and beat in egg and vanilla.
Spread half of chocolate batter in the baking pan, layer with cream cheese filling, then top with the remaining chocolate batter. Bake brownies in middle of oven 45 to 50 minutes, or until a toothpick inserted in center comes out clean. Cool brownies completely in pan on a rack. They can be served cold or at room temperature, but refrigerate any remaining brownines.