Position a rack in the middle of the oven and prehat to 350° F.

Grease three 9-inch cake pans iwth butter.  Line the bottom of each with a round of parchment. Grease the parchement. Lightly flour the bottom and sides of the pans and set aside.

Cream 2 sticks of butter wtih the sugar until light and fluffly.  Add the eggs one at a time, beating well after each addtion.

Sift the flour with the baking powder and salt.

Working in alternating batches of three, add in the flour mixture and the milk, beating well after each addtion.  Add the vanilla.  Using a rubber spatula, scrape the bottom of the bowl and fold in the batter so you have an even mixture.

Divide the batter evenly among the prepared pans then gently tap the pans against the counter to release any air bubbles.  Bake for 20 mintues until golden and test done with a tooth pick. Remove from the oven and allow to cool in their pans for 10 mintues before inverting onto greased cooling racks. 

To make the Caramel Icing:

Heat 3 cups of the sugar with the corn syrup and milk in a medium pan over medium heat until sugar dissolves.

Add the remining 1/2 cup sugar to a large heavy bottom pot set over medium heat and cook, swirling until ambler.  Carefully add thewarm milk mixture (it will bubble and rise).  Stir the mixture then heat undisturbed to 240º F when measured with a candy thermometer, about 5 to 10 minutes.  Remove from teh heat then stir in the butter, vanilla and cream until the butter is melted then allow to cool undisturbed until the temperature has dropped to 180° F, about 20 minutes.

Beat the caramel with a hand held electric until thickened, about 10 to 12 minutes.

To assemble the cake:

Place 1 cake layer on a cake plate or stand. Slowly pour some of the caramel icing on top of the layer, spreading out to the edge of the cake with an offset spatula. Top with the second cake layer and repeat.  Add the final layer.  Pour the remaining icing over the top using the spatula to even the icing and spread down the sides.  Continue to cover the cake with any icing that pools on the bottom.  As the icing continues to cool it will set.

Allow the cake to sit for 1 hour before slicing.