Remove butter from refrigerator about 2 hours before mixing cake batter. Have all other ingredients at room temperature.
Position rack in lower third of oven and preheat to 325º.
Grease and flour a Fleur-De-Lis cake pan or 10 cup tube pan.
Place sour cream and milk in a small bowl and stir to blend; set aside.
Place butter in the bowl of an electric mixer and stir flour, sugar, salt and baking powder into bowl over butter. Add eggs, vanilla extract and sour cream mixture.
Using an electric mixer, preferably with a K-shaped beater or paddle attachment, beat on low speed until creamy and smooth, 1 1/2- 2 minutes; stop mixer and scrape bowl.
Fold in ginger and apricots by hand.
Spoon batter into pan and spread batter up to the pan rim.
Bake until cake springs back when lightly touched in the center and a toothpick inserted in center comes out clean. 55-65 minutes.
Transfer to a cooling rack and cool cake upright in pan for ten minutes.
Tap sides and invert cake onto a wire rack set over a sheet of waxed paper.
To make the glaze, in a small bowl, blend together rum, water and sugar. Using a pastry brush, brush surface of warm cake with glaze.
allow the glazed cake to cool completely, 1-2 hours before serving.