Preheat oven to 350°. Line bottom and sides of a 9-inch square pan with aluminum foil, allowing 2 to 3 inches to extend over sides; lightly grease foil.
Microwave chocolate squares and butter in a large microwave-safe bowl at HIGH 1 1/2 to 2 minutes or until melted and smooth, stirring at 30-second intervals. Whisk in brown sugar and 1 1/2 cups granulated sugar. Add 3 eggs, 1 at a time, whisking just until blended after each addition. Whisk in vanilla, salt, and 1 cup flour. Spread half of batter in prepared pan.
Beat cream cheese at medium speed with an electric mixer until smooth; add 2 tablespoons flour and remaining 1/4 cup granulated sugar, beating until blended. Add bourbon and remaining 1 egg, beating until blended.
Pour cream cheese mixture over brownie batter in pan; top with remaining brownie batter, and swirl together.
Bake at 350° for 40 to 45 minutes or until a wooden pick inserted in center comes out with a few moist crumbs. Cool completely in pan on a wire rack (about 1 hour). Lift brownies from pan, using foil sides as handles. Gently remove foil; cut into squares.