Heat oven to 350 degrees Fahrenheit. Grease a 13x9-inch baking dish.
In a large microwaveable bowl, melt butter. Stir in sugar and vanilla with a spoon. Add eggs, one at a time, mixing well after each addition. Add cocoa; mix completely. Add flour, baking powder, and salt; mix well. Pour into prepared baking dish.
Bake 30 to 45 minutes (depends on type of pan used; metal vs glass) or until a toothpick comes out almost clean from the center and the edges are pulling away from the sides of the pan. Cool completely.
FOR THE FROSTING: Using an electric hand mixer, beat the butter, cocoa, corn syrup, and vanilla in a large bowl. Add the powdered sugar, 2 Tablespoons of milk, and a pinch of salt. Mix well. Add more milk a little at a time until desired spreading consistency is reached. Frost cooled brownies. Cut and serve. Cover any leftovers and store at room temperature.