Preheat oven to 350°F. Butter a 9×13-inch baking pan or two 8×8-inch square pans.
Cream butter and sugars until fluffy.
Beat in eggs and vanilla.
Combine flour, cocoa, and salt. Fold dry ingredients into creamed mixture by hand to moisten dry ingredients and avoid dusting; then mix until well blended.
Spread mixture into prepared pan.
Bake 15 to 17 minutes or until the center of the brownies are mostly set.
Blend cream cheese and sugar until well blended.
Add lemon juice and mix well.
Add eggs mixing just until blended.
Pour cream cheese topping evenly over brownie base.
Drizzle melted chocolate in small pools over the cream cheese topping. Use the tip of knife to drag through the chocolate in a grid pattern. Swirl slightly to give a marbled effect.
Bake 20 minutes or until center is almost set. Cool to room temperature then refrigerate for 4-5 hours. Cut into bars.