Grease and flour three nine-inch round cake pans and preheat oven to 350 degrees.
Cream the butter with both granulated sugar and light brown sugar until very light and fluffy, then add the eggs, one at a time, beating well after each addition.
Sift the flour with the baking powder, baking soda and salt and add to the batter alternately with the milk, beginning and ending with the dry mixture. Stir in the vanilla extract.
Divide batter evenly among the prepared pans and bake in the center of the preheated oven for 25 to 30 minutes or until a wooden pick inserted in the center of the layers comes out clean. Cool layers in their pans over a rack for ten minutes, then loosen and turn out layers directly onto racks for cooling. Cool layers thoroughly before icing.
For the icing, melt the butter in a large saucepan over medium heat. Remove from heat, then stir in granulated sugar and light brown sugar. (Sugars will not dissolve).
In a separate bowl, whisk the egg yolks with the evaporated milk until smooth, then whisk this mixture into the saucepan with the sugar mixture. Return saucepan to a medium heat setting and cook, whisking constantly, until mixture is thick, shiny and caramel-like, about 15 to 20 minutes. Remove from heat and stir in vanilla extract and pecans.
Cool icing to a good spreading consistency (about 30 minutes), then spread evenly between cooled cake layers and over the top and sides of the cake.