Preheat the oven to 350 degrees F. Spray an 8x8-inch pan with nonstick spray.
PREPARE THE BROWNIES:
In a medium bowl, use an electric mixer to mix the butter sugar, egg and vanilla. Stir in the flour, baking powder and salt, just until incorporated. Spread the batter into the prepared pan. Bake for 25 minutes. Remove from the oven and let cool in the pan.
PREPARE THE ICING:
When the brownies are just about finished baking, prepare the icing. In a small saucepan, melt the butter and cook until brown, stirring constantly. Add the brown sugar and continue cooking, stirring until the sugar is completely dissolved. Pour in the half and half; stir. Remove from heat and set aside to cool.
When cooled a bit, add the powdered sugar (use your judgment on how much- according to thickness), vanilla and salt. Beat until thick. Pour the icing over the brownies, and set them aside to let them cool completely. It's okay to refrigerate them to speed up the process.
I find it easiest to remove the whole slab of frosted brownies to a cutting board. Just stick a knife on the side, and they should lift up pretty easily. Cut into squares. Keep leftovers in a covered container for up to 3 days.