Combine sour cream and milk in small bowl; set aside.
Beat butter until creamy; gradually add sugar, beating well.
Add eggs, one at a time, beating well after each addition.
Sift flour, baking powder, and salt; add to butter mixture alternating with sour cream mixture, beginning and ending with flour mixture.
Stir in vanilla (and rum extract).
Pour batter into prepared pans.
Bake in heated oven for 30-35 minutes, or until toothpick comes out clean.
Let cool in pans 10 minutes; remove from pans, and cool completely on wire wracks.
For frosting: Combine 2 1/2 cups sugar, milk, beaten egg, and salt in a bowl, stirring well; stir in butter.
Sprinkle remaining 1/2 cup sugar in saucepan; cook over medium heat, stirring constantly, until sugar melts and syrup is a light golden brown.
Remove from heat.
Stir butter mixture into hot caramelized sugar.
(The sugar mixture will tend to clump, but will become smooth after further cooking.) Cook entire mixture over medium heat, stirring constantly, until candy thermometer registers 235* (about 15-20 minutes).
Cool mixture for 5 minutes.
Beat frosting with a wooden spoon to almost spreading consistency (about 5 minutes).
Immediately spread between layers and on top and sides of cake.