Melt first 3 ingredients in a small saucepan over medium-low heat, stirring occasionally. Cool.
Stir coffee granules into hot water until dissolved. Cool.
Beat cream cheese and 1/4 cup butter at medium speed with an electric mixer until creamy; gradually add 1/2 cup sugar, beating well. Add 2 eggs, 1 at a time, beating until blended. Stir in coffee and 1 teaspoon vanilla. Fold in 2 tablespoons flour and 1/2 cup chocolate morsels; set batter aside.
Beat remaining 4 eggs in a large bowl at medium speed; gradually add remaining 1 1/2 cups sugar, beating well. Add melted chocolate mixture and 2 teaspoons vanilla; beat well. Combine 1 cup flour, baking powder, and salt; fold into chocolate batter. Stir in remaining 1 cup chocolate morsels.
Spread half of chocolate batter evenly in a greased 13" x 9" pan. Pour cream cheese batter over chocolate batter. Top with remaining chocolate batter; swirl with a knife.
Bake at 325° for 45 minutes (wooden pick will not come out clean). Cool completely in pan on a wire rack. Cut into squares.
Note: Line your pan with aluminum foil to ensure pretty squares and easy cleanup.