Adjust rack one-third up from bottom of oven. Preheat oven to 350 degrees. Butter a 9 x 3?-inch tube pan (or two loaf pans). Sift together flour, baking powder, and salt and set aside. Combine milk and rum and set aside. In large bowl of electric mixer cream the butter. Add the sugar and beat for 2 to 3 minutes. Beat in the eggs individually, scraping the bowl as necessary with a rubber spatula to keep mixture smooth. On lowest speed alternately add the dry ingredients in three additions and the milk/rum in two additions, scraping the bowl with the rubber spatula as necessary and beating only until smooth after each addition. Stir in grated ginger. Turn the batter into prepared pan(s). Level top by gently shaking pan back and forth.
Bake for about 65 minutes until a cake tester comes out dry. Let cake stand in the pan for about 3 minutes and then cover with a rack and invert. Remove pan, leaving the cake upside down. Place over a large piece of aluminum foil or wax paper and prepare glaze.
GLAZE: 1/3 cup rum, 1-2 tablespoons sugar
Stir the rum and sugar together and brush all over the hot cake until absorbed. If using loaf pans, turn the cakes over and brush the tops too.
Do not cut cake for at least several hours.
To make ginger-flavored rum, soak slices of fresh ginger in rum for at least a week. The alcohol will preserve the ginger for a very long time. I keep using the ginger from the jar and then just add more to keep the flavor consistent as I use and then add more rum too.