Preheat oven to 325ºF. Butter and flour two 8×4-inch loaf pans, knocking out excess flour. Mix the flour, baking powder, and salt together in a bowl. Set aside.
Beat the butter in the bowl of an electric mixer on medium speed for 3 minutes, until whipped looking. Slowly add the sugar and beat for another 3 minutes, increasing the speed to medium-high. The mixture should look very light and fluffy. Add the eggs one at a time, beat well after each one. Scrape down the sides of the bowl and beat again.
Combine the milk with the vanilla. Add the flour in 3 portions alternately with the milk, beginning and ending with the flour. Fold the last flour addition in by hand with a rubber spatula. Turn the batter into the prepared pans. Bake for 1 to 1½ hours, checking after 55 minutes and every 5 to 10 minutes thereafter, until a toothpick inserted near the center of the cake comes out with just moist crumbs attached. If the cake is very brown after 55 minutes but not yet fully baked, cover the top with a sheet of aluminum foil. When done, the cake will be springy to the touch and pulling away from the sides of the pan. Let cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely before glazing.
Melt the butter in a heavy-bottomed saucepan over low heat, then add the brown sugar and raise the heat to medium. Boil, stirring constantly, for 2 minutes. Add the milk and return to a boil, stirring constantly. Remove from heat and stir in the salt and vanilla. Let cool for 10 minutes.
Sift 1 cup of the confectioners’ sugar over the mixture, stirring with a whisk until smooth. If the glaze is thick enough for your liking, you can stop there. If not, sift the additional ½ cup sugar in. Place the cake (still on the wire rack) over a wax paper lined baking sheet. Pour the glaze over the cooled cake and allow it to drip down the sides. Allow the glaze to set completely before slicing and serving. Wrapped carefully, this cake will keep for several days at room temperature. If you happen to have some homemade caramel sauce on hand, it is amazing poured over top.