Preheat the oven to 325 degrees F (165 degrees C). Grease and flour a 10-inch tube pan.

In a large mixing bowl, cream together 1 cup of butter (or margarine), shortening, brown sugar, and 1 cup white sugar. Add eggs one at a time, beating well after each addition. Stir in 1 teaspoon of vanilla.

Sift 2 1/2 cups of flour and baking powder. Add alternately with milk to the creamed mixture. Stir 1/2 cup of flour with the chopped pecans, then fold into the batter. Pour into the prepared pan.

Bake in preheated oven for 60 to 90 minutes, or until a toothpick inserted into the center comes out clean. Let stand in the pan for 10 minutes, then turn out onto a wire rack and cool completely.

To Make the Frosting: In a small saucepan, combine 1 cup brown sugar, 1 cup white sugar, butter (or margarine), and milk. Bring to a rolling boil and cook for one minute. Remove from heat, and stir in vanilla. Cool, then beat until thickened. Add a little milk if it's too thick. Spread on the cake.