Prepare Cream-Cheese Filling; set aside.
Preheat oven to 350°F Grease an 8- or 9-inch-square baking pan.
In a medium saucepan, combine butter or margarine and chocolate pieces.
Heat over low heat until melted and smooth, stirring constantly. Remove from heat.
Stir in sugar, eggs, water and vanilla until combined. Add flour, baking soda and salt, stirring well. Stir in walnuts, if desired.
Spread half the chocolate batter evenly in greased baking pan. Top with Cream-Cheese Filling, spreading evenly.
Drop spoonfuls of remaining chocolate batter evenly on top of cheese filling, spreading as evenly as possible with a knife. Swirl knife gently through batter to marble.
Bake 30 to 35 minutes. Do not overbake. Brownies should be moist in center. Cool in pan.
Cut cooled brownies into squares. Store in refrigerator.
Cream-Cheese Filling: In a small bowl, beat cream cheese, sugar, egg and vanilla until smooth.