Preheat oven to 350º F. In a medium saucepan cook chocolate chips and butter over low heat, stirring often, until melted. Remove from heat and allow to cool slightly.
Brownie mixture: In a large mixing bowl or with hand mixer, beat 2 of the eggs on medium speed until foamy, 3-5 minutes. Add 1 ¼ cups sugar, water, and 1 teaspoon vanilla. Beat on medium speed, about 5 minutes until slightly thickened and light-yellow color. Beat in melted chocolate mixture until combined. Hand stir in 1 cup of flour, salt and baking powder, then stir in toasted pecans. Set aside.
Cheesecake mixture: In a separate medium bowl, beat the remaining 2 eggs, 1 teaspoon vanilla, 2/3 cups sugar, 2 tablespoons flour, cream cheese, and lemon juice until smooth.
Prepare a 13x9x2-inch baking pan by lining bottom and up the sides with foil, grease foil. Pour half of the brownie mixture into the pan and spread evenly. Carefully spread all of the cheesecake mixture evenly over the brownie mixture. Spoon small amounts of the remaining brownie batter over the cheesecake layer (see photos above in post). Then using a butter knife, gentle swirl just until marble pattern forms.
Bake for 45 minutes at 350º, or until knife or toothpick inserted comes out clean. Cool slightly, then remove brownies by lifting edges of foil. Cut into squares.