Pour 1 1/4 cups sugar into a jar. Split vanilla bean in half lengthwise. Scrape tiny vanilla bean seeds into sugar; cut bean into 1" pieces, and add to vanilla sugar. Cover and shake vigorously to mix, or stir well. Let stand 24 hours.
Combine flour, baking powder, and salt; stir well. Beat butter at low speed of an electric mixer until creamy. Remove and discard pieces of vanilla bean from sugar. Gradually add vanilla sugar to butter, beating at medium speed until light and fluffy. Add eggs, one at a time, beating well after each addition. Gradually add flour mixture to butter mixture, beating at low speed just until blended.
Pour batter into a lightly greased and floured 9" x 5" x 3" loafpan. Bake at 325° for 1 hour or until a wooden pick inserted in center comes out clean. Let cool in pan on a wire rack 15 minutes.
Meanwhile, combine powdered sugar, milk, and vanilla extract; stir well. Prick tiny holes in top of loaf with a wooden pick. Spoon glaze mixture over warm loaf; let cool in pan on a wire rack 15 additional minutes. Remove from pan, and let cool completely on a wire rack.
Note: Don't be intimidated by vanilla beans. Find them as leathery brown beans folded in a narrow glass tube or bottle on the spice isle.