*Grease and flour 2 9" cake pans. Preheat oven to 350 degrees F.
*Mix 1/2 cup softened butter with 1 cup packed dark brown sugar with a mixer for at least 4 minutes. Sugar will disappear into the butter completely. Whip in the vanilla extract.
*Add 3 eggs one at a time, mixing well after each addition.
*Separately, sift together the cake flour, self-rising flour, baking powder and salt. Add the box of instant pudding mix and toss lightly with fork.
*Add the dry ingredients alternately with the milk to the sugar-butter mixture. After the last addition, beat the batter for one additional minute. Then, pour the batter into the two pans.
*Baking time: 30 minutes. Cool layers completely before frosting.
*To make the caramel frosting: Melt the butter in a heavy saucepan and stir in the brown sugar. Turn up heat to medium and bring to a rolling boil. Reduce heat and cook for 2 minutes. Take off heat and allow to cool for 5 minutes.
Add the heavy cream and vanilla & pour into mixing bowl. Beat with electric mixer for 2-3 minutes. Add in 10X sugar a cup at a time and beat on medium speed after each addition, adding a drop or two of extra cream as necessary. Frosting will be thick, but spreadable. If as you frost the cake the caramel frosting becomes too thick to spread, add another drop or two of cream.
*Refrigerate uncovered frosted caramel cake for at least 3 hours before serving. Remove from refrigerator at least 3/4 hour before serving. Store leftovers (should there be any!) tightly wrapped or covered.