Heat oven to 350 degrees. Grease bottom only of a 12/9 inch pan.
BROWNIES: In a large bowl combine brownie mix, 1/4 cup of Bailey's, oil and eggs. Beat 50 strokes with spoon. Spread into greased pan.
Bake at 350 degrees for 28 to 30 minutes or until set. Do not over bake. Cool one hour or until completely cooled.
FROSTING: In a small bowl beat 1/2 cup butter until light and fluffy. Beat in powdered sugar, vanilla, 2 tablespoons Bailey's, and milk, adding enough milk for desired spreading consistency. Spread over cooled brownies.